The Roman Empire influenced it's future history as no other empire before or since.:
GOVERNMENT:
The Roman Empire has given most of the modern world and much of the medieval world it's governments in not only it's forms but also in it's substance. The barbarian tribes who sucseeded the empire adopted much of it's laws and many of it's forms of governments. For instance the Visigoth kingdom of Italy had a senate and for a time consuls. The Roman Catholic Church and the Byzantine Empire which followed Rome had many of the titles of Rome(eg: Poniffus Maximus-the Pope's title was the old Roman title of the chief priest of Jupiter). And the Byzantine Empire having developed as from the Eastern Roman Empire had all the trappings of Roman government save the democratic substance.
The influence has been greatly felt in our modern world. The Romans had the Plebian Assembly(the assembly of the common people and the Centurie Curiea (the assembly of the men grouped into centuries to vote in time of war) This corresponds to our common or lower house(the house of commons in Britain and congress in the United States) They also had an upper house-the Sentate-a house of review and in the republic, the virtual rulers. This corresponds to the upper house-the house of lords in Britain and the senate in the United States. Most countries of democracy in the world have similar organisations. Also the Roman Tribunes(officers of the people) are in correspondance to the ombudsman of many western countries. And also the Roman Empire right up to towards the end had the common touch which is indicitive of many of the countries in the world today.
PHILOSOPHY:
The Roman Empire had influence in two main areas of philosophy. One, the general subject of philosophy itself and two, the type of philosopy it has past down to the western world. The Romans were great copiers and looters. They looted everything including abstract ideas. And philosophers, For instance Epictitus was a Greek slave who earned his freedom and went up in the world. His philosophies stemmed from the stoicism of Zeno of Citium(in Cyprus) throught to Crispus and Cleithenes (although much more like Crispus) to influence writers like the emperor Marcus Aurelius throught to the present day. They kept alive the philosophies of Greece and passed them on to us through the Byzantine Empire and the East. They were instrumental in the introduction of Christianity to the west-to us.
But the Romans also taught us their unique philosoph. They taught us that great power could be used with humility and humanity. Previously except for the Greeks and sometimes the Israelites, power and majesty were synomomus with pride and semi worship. Although the Roman emperors were mostly diefied after their death they and their empire had a democratic spirit that has really only come in the twentieth century to most of the world. They had various offices which took care of the people. For example the Tribunes whoes persons were sacrocent. Untouchable because they represented the people. The Caesars although so called monarchs were really first citizens and almost absolute rulers of what was really a republic which called itself an empire. The emperors mostly did come to the throne through merit and considered themselves as human as everyone else. When you were before Caesar as a citizen appealing your case, and the emperor couldn't refuse, and the case was going or gone against you-it was tradition to abuse the Caesar. For instance when a philosopher was losing his case before Commodus he said that Commodu's father-Marcus Aurelius was a true emperor-Commodus-a spoilt little boy. Commodus and even other bad emperors accepted this. When people were writing on Nero's statues, "this is a real competiton Nero, and you've just lost" , pointing to Nero's special love and faith in his artistic talent, Nero did not bear them any grudge. There was an absent of pretence in Roman philosophy the likes that would make modern governements blush. The emperor stood at the head of the Roman Empire-but above the emperor-stood the mob.
The Romans took care of their people to . For slaves there was generally better treatment than in other empires and mostly, but not always, than even the Greeks. There was a path to freedom by manumission, a will, declaration by the emperor or by saving the monies that you occationally or even regularly mostly recieved and buying it. There was a path to citizenship itself. A freed slave could spent five years in the Vigiles(the fire brigade in Rome) and then would recieve citizenship. Claudius I (Calighula's uncle) decreed that any slave who was abondonded and sick and recovered was free. For the provincal there was protection under law, the opportunity to join the auxiluries for 30 years and become a citizen and infrastucute built such as aqueducts. For the citizen there was rights under law such as the appeal to Caesar, political rights and the famed bread and circuses. The Romans gave us the idea of taking care of our people in an organised fashion and providing relief in times of hardship. They introduce the idea of grandeaur and imperium, of magnificance on a grand and civic scale. The idea of public amenities such as libraries and hospitals, of vast public entertainment-eg: the Colloseium. They inroduce the idea of toughening it out when things are down. In history most powers when decively defeated fell. Rome introduced the idea of fighting on. For instance Rome came back from Cannae, the destruction of it's largest field army at the hands of Hannibal, to win the second punic war. After Cannae boys and slaves guarded the walls of Rome for a bit. America came back from Pearl Harbour to win World War II. And all the representations of our idea of imperium, of empire, of magnificance, of sheer b****y power comes from Rome. From the old ideas and actual practical examples of the old films (eg: The Great Dictator) to Star Wars-the spirit, the hand of Rome behind the scenes is ever present. They lifted up the west and gave it the idea, the concept, the practicality and the way of greatness.
LITERATURE:
The impact of Roman litrature influenced the subsequent and modern world like no other. It not only preserved much of the wisdom of the ancients, but also in educated circles (such as monestaries and the east) Roman litrature was widely read. The philoposphies of Marcus Aurelius, Epictitus and Epicurius, the histories of Livy, Pliny, Sullust, Suetonius, Volcanus and Vegitius, the poetry of Virgil and Ovid, the poetry of Martial and Juvenul as well as their commentaries on daily life of the period-all these are well read through history and have influence greatly our literature in their style and basic idea. Many people, especially of my generation have, if not actually read, have at least heard of these authors. And they are very well read by many people today.
But the greatest impact in the area of literature that the Roman Empire produced is in the area of our literiture. Not only have our films been influence but we have made so many films about or associated with the Roman empire. Many of the great epics of the 1930s, 1940s, 1950s and 1960s have been about Rome. And mostly they are the goodies and even in films about Jews or Christians, Rome is mostly figured largely and most of the time, even if they are the villian, they win. Such was their power and reputation. Tons of books have been written about them from Gibbon's "Decline and Fall of the Roman Empire" to modern authors such as Colleen McCullen. Plays have been written about them and this modern world is chock a block full of litrature about them. Such was their long history, their influence and their magnificance that they could not fail to influence and impact upon our modern world as such as they have.
Why the Roman Empire lasted so long? It was very very powerful. But why was it very very powerful? There are many reasons. For one, it started out as a collection of villages or a bandit stockade of tough backwoodsman. They had the philosophy of courage. They feared and bowed to no tyrant. When their last king Tarquinius Superbus offended them-they overthrew him and declared a republic. Something so rare, especially in those times. They had both a philosophy of humanity and humility. They would treat their subject peoples better than anyone. In the republic they made treaties with them fairly and the reason why Hannibal found it so hard to get allies in Italy was the fair way Rome treated the peoples under it. In the empire they treated the people with a basic fairness and gave them opportunity. They didn't have many prejudices. And any enemy who did defeat them in battle-they learnt from. They were not too proud to acknowledge a learn. They lean't the pilum from the Samnites. The learnt the quinqunx(flexalbe formation) as a result of defeats by the Gauls. They learnt naval power from the Carthaginians. They also learn't the pincer movement from Hannibal. They learn't the use of massed cavalry from some barbarians. They lean't the stirrup from the Sassaniad Persians. All thoughout history they learnt and won.
Also they had an empire which was so organised and practical that for centuries it gave it's people peace, protection, prosperity and purpose. After centuries the peoples had become romanised. They accepted everyone who would come. All were welcomed to participate in the great adventure that was the Roman Empire. Also they had the most terrifying army in history. Their legions were organised into three rotating lines of lethal military teeth, organised into both breadth and depth attack and defence efficiency with flexable organisation for both defence(an enemy would be trapped in the formation) and attack(maximum manouverbility). Behind them they had a "double" reserve cohort, the primi cohorte, with the best men in legion commanded by the chief centurion-the primus pilus interta. They were equipped with short throwing spears(pilums) developed so when it struck an enemy's shield it snapped, bent down, weighed the shield down and made it useless. They were equipped with a sword engineered in such a way that it was the most terrifying cutting weapon in history. Their shields were of hard wood, boiled leather(extremely hard) and metal. Could take anything the ancient world could throw at it.
They were backed up by legionary and auxilury cavalry, legionary and auxilury slingers, archers, spear throwers, dart throwers, light infrantry, medium infranty, transport, supply, logistic, fire, medical, command, scout, spy, technical and engineering units and had something that no other ancient army had. Field Artillery. Sixty catipults(arrow and spear throwing), ten ballista(rock and incendury throwing-with range of up to 400 yards with 360 pounds) and the dread raspioballistas(giant cross bow like throwers of huge bolts designed for mowing down ranks) They were commanded by experience centurions, aptly organised and with vast combat experience. Many of their senior officers and generals were talented and experience. Some of their commanders were great. And they concentrated on training like few other. Two years basic training(the Amura) and three advanced (the Armabillica) with continuous training in physical, drill, weapons, march, manouvers, formations, engineering, garrison and military exsicises they were the best trained amry in history. As Josephus said, "they march as one" and "they do not allow peace time to soften them. They continuously prepare for war. Their manouvers are bloodless combat, their battles are sagunary manouvers". They actually built a fortified camp when on the march, something no one else did. And their turlte(torquedos) a formation of shields covering the men was, when fully trained, tested with a fully armed war chariot drawn by two horses, standing on top of it. And they were backed up by a nation and government that in it's philosophy of care of the military was the most organised power in history. For instance their collosium had an underground complex with lifts, cages, equipment, pulleys and entrances, shops, artwork, leisure areas, a movable roof in case of rain, 82 entrances and a seating system that was organised into tiers and section coordinating with the enterances that enabled normal evacuation in the unbelievable time of literally 200 seconds. A time and efficiecncy beyond even the best of modern stadiums. And when they besieged Masada in the Jewish Wars, they sent a giant siege tower up a built up natural ramp up a mountain. As it went up the angle, gears in the back adjusted the thing to have a centre of gravity equal to that of the angle of the ramp. With such wonders it is no wonder that this wonder, the Roman empire, seemed like it would never cease.
You see, whilst many other people have and still do - consentrate on a lot that drains and uses energy, the Romans were practical and humble enough to concentrate upon the things that were important. The things that worked. By a combination of humility, humanity, leadership, technology, organisation, training, the backing up of huge rescourses(eg: Tiberiu's personal fortune was between 2,700,000,000 and 3,300,000,000 denarii and in the later empire they paid 100,000,000 sectercii per year for silk alone), the backing up of an extemely efficient government organisation, a vast industial, shipping, transport(eg:their roads)and economical system and by sheer b****y grit and determination they held for so long the mightiest empire(for it's time of course) the world has ever known. And off course the belief in itself. For when that was lost-all was lost. What it took to fall this giant of giants-this collossus - plague, natural disasters, waste by the emperors, civil war and strife, military defeats-contributing a bit, introduction of christianity(sapping of military and civic spirit), bad social and financial edicts, bastardisation of the legions and the army, the freezing over of the Rhine(tribes pouring across), the weakness of the emperors, the division of the empire, the betrayal of it's last field army, the fact that the barbarians began to treat people better, high taxation, the barbarian promised a brave and refreshing new world, the loss of belief in Rome and the fact because of inate conservatism-history's verdict that it was this empire's time to go. A lot, and more, and still more and still a lot more. What it took to fall this empire indeed. What it took would account for half the empires in hisory. Rome had so many causes for it's fall and sucsessors-both immidiate and eventual. By inheritance and influence. More than any in history-much much more. For all this it is no wonder that at the time people thought Rome was the world, that so much has been written about it and it is no wonder that Rome is commonly know as the ultimate empire. It is no wonder that such took lasted so long. It's actual physical existed for well over a milenium. How long will it's influence last-whoes to tell.
Hope this helps.