This answer concerns the pyramids constructed in ancient Egypt and Nubia. Pyramids or pyramid-like constructions were built at different times in different parts of the world.
Pyramids in Egypt served as tombs, initially only for kings and close members of the royal family, but eventually came to be used (in much smaller forms) by the general populace.
As for aliens or the supposed "lack of ability" on the part of the Ancient Egyptians to be able to build pyramids:
The Egyptians were perfectly capable of using the basic mathematics necessary for the construction and layout of most pyramids. Despite the superb accuracy of the layout and plan, this was not impossible for them to achieve, nor did it require calculus. While no mathematical texts from the Old Kingdom survive, texts from the Middle Kingdom and Second Intermediate Period demonstrate a clear familiarity on the part of the Egyptians with basic arithmetic, geometry, and trigonometry.
There is absolutely no evidence that alien help was needed to construct the pyramids, which were intended as tombs for Egyptian kings.
Some of the best evidence for human responsibility, and specifically Egyptian human responsibility dating to the 4th Dynasty, for the construction of pyramids comes from the site of Giza itself. Giza is the place most people think of when they think of Egyptian pyramids, though there are numerous pyramids in other areas of Egypt and Nubia and the Giza pyramids are by no means the earliest pyramids constructed in Egypt.
Also of significance are a number of inscriptions associated with the so-called "Great Pyramid" of Khafre at Giza. One of the inscriptions on a stone block making up the pyramid gives the name and regnal year of Khafre. Others bear the names given to crews of workmen responsible for moving the stone blocks into place. At least one of these inscriptions is located in an area almost impossible to reach - frequently the inscription is examined using a mirror - thus making it highly unlikely that it was a later addition.
As you mentioned the so-called "scholar" Graham Hancock, who has admitted himself that he has no training in archaeology and holds a degree in Sociology, I will point out that he has been taken to see these informal inscriptions on the blocks within the Great Pyramid and even he admits that must be original to the building and not placed there long after the pyramid was constructed.
As for the so-called "stellar alignment" that Hancock among others has posited, wherein the major Giza pyramids are said to align with Orion's Belt, noted astronomer Dr. Ed Krupp has pointed out that the theory only works if you flip the cosmos so that north faces south. Dr. Mark Lehner, one of the foremost scholars in the field of Egyptian pyramid studies, also notes that when the map of Orion is positioned over a map of Giza, there are stars in Orion for which there is no corresponding pyramid and there are pyramids for which there are no corresponding stars.
As for other theories not accepted by professional Egyptologists:
They were not storehouse for grain, though a sort of conical shaped storehouse for grain are attested in ancient Egypt and it may be that these led to the bizarre claim that the pyramids (usually meaning just the pyramids at Giza, ignoring the presence of numerous other pyramids throughout Egypt) were storehouses for grain and that they were the storehouses mentioned in the Bible in connection with the story of Joseph.
As for the tradition that the Jews built the pyramids, the time period in which the vast majority of royal pyramids were constructed predates (by as much as 1000 years) any attestation of a group of people known as "Jews," "Hebrews," or "Israel." As described below, the labor organization used to construct the pyramids was distinct from slavery. If there was a time of slavery for the Jews in Egypt as attested in the Old Testament, it probably post-dated the construction of most royal pyramids. And the Biblical texts themselves refer to cities located primarily in the Eastern Delta as the places where the Jews are said to have lived and served as slaves. There have been no pyramids found north of Giza, near Cairo which is south of where the Delta begins.
Pyramid construction in Egypt began around 2600 BC, the last known royal pyramid was built in Egypt around 1550 BC. The time of the Exodus is usually regarded as having been in the 19th Dynasty of the New Kingdom (usually the 19th with the king being Ramses II) in ancient Egypt.
Thus, if Ramses II was "Pharaoh" of the Exodus, it occurred between 1282 and 1213 BCE (depending on which chronology you go with; there's a margin for error of about 20 years).
Some have suggested an even earlier date in the reign of Thutmoses III, around 1472-1426 BC.
Regardless of which king you prefer, this is still 1000 years after the construction of the first true pyramid as well as the pyramids at Giza.
In addition, the first reliably dated inscription naming a group of people/nation called "Israel" is the Merenptah Stela. Merenptah reigned between 1213 and 1203 BCE.
I might also add that in the New Kingdom (with a few possible exceptions) and up until the Late Period, Egyptian kings were buried in rock-cut tombs in Luxor/Thebes in the Valley of the Kings. If the Jews were in captivity in Egypt they wouldn't have been building pyramids. And, as note above, they probably wouldn't have been anywhere near Thebes, which is in the southern part of the country. There is also extensive evidence and the settlement of the workmen who worked on the royal tombs in the Valley of the Kings and they were not slaves, nor do they appear to have been anything other than Egyptians.
General History of Pyramids in Egypt and Nubia:
The pyramid is thought to have developed out of the mastaba tomb. Mastaba is an Arabic word, meaning bench, which was applied to the flat-topped, slope sided superstructures of tombs. The pyramid is also thought to be associated with solar worship and the "ben-ben" stone which played a major role in sun worship and was vaguely pyramid shaped.
In the 3rd Dynasty, several mastabas were stacked forming the Step Pyramid of King Djoser. By the 4th Dynasty in the reign of Snefru attempts at building a true pyramid were underway. The pyramids of the 4th and 5th Dynasties, including those at Giza, essentially reflect the further refinement of the pyramid, the chambers within it, and the associated temple complexes. Eventually the standard style was an orientation of east to west (significant in Egyptian religion), with a pyramid temple, located directly on the east side of the pyramid, and a causeway leading to the "valley temple" located near the Nile at the edge of the cultivation.
While it is accepted by reputable Egyptologists that pyramids served as burials for kings, the exact details of the theology behind them remains unclear. One idea, popularized I believe by Dr. Mark Lehner, one of the foremost experts on Egyptian pyramids, is that pyramids served as "resurrection machines" providing all the necessary means for eternal life with the gods for the dead king.
In the late 5th Dynasty in the Pyramid of Unas at Saqqara, we have the first appearance of formal texts within the pyramid itself - the appropriately-named Pyramid Texts. These texts are somewhat esoteric and are essentially a collection of spells, stories, and guides relating to the Underworld. Initially these texts were limited to royalty. In succeeding pyramids, elements of the Pyramid Texts were included in the "Coffin Texts" of the First Intermediate and Middle Kingdom and in the "Book of the Dead" of the New Kingdom - texts available to a broad spectrum of society.
Pyramid construction continued in the Middle Kingdom - again limited to royalty, but not on the grand scale of the Old Kingdom. The last known royal pyramids located in Egypt are that of King Ahmose, founder of the 18th Dynasty of the New Kingdom (ca. 1550 BCE) and the pyramid-cenotaph constructed for his grandmother, Queen Tetisheri. Both are located at Abydos.
In the New Kingdom, pyramids came to be part of tombs for reasonably wealthy private individuals - frequently added to the exterior portico area of rock-cut cliff tombs or appearing as architectural elements of brick constructed tombs in varous parts of Egypt.
The Napatan and Meroitic kingdoms in Nubia (modern Sudan) also used the pyramid for royal burials at sites such as El-Kurru and Nuri. While the Napatan kings ruled Egypt for a time during the 25th Dynasty and were buried in pyramids, those pyramids were located in Nubia proper.
Pyramid Construction:
Pyramid construction relied on highly skilled teams of workmen who were housed nearby the pyramid fields - in the Old Kingdom located in the general vicinity of the ancient capital Memphis at sites now knows as Giza, Saqqara, Meidum, and Dashur. A few pyramids in the Middle Kingdom were located near the Fayum, roughly Middle Egypt.
In addition to the full-time workmen, there was likely a seasonal labor requirement asked of the lower classes of Egyptian society - a sort of taxation, often referred to by the French term "corvee" labor. This is distinct from slavery. While the ancient Greek historian Herodotus (writing over a thousand years after the construction of the pyramids at Giza) reported that he was told the pyramids at Giza were constructed by slaves, Herodotus was wrong about any number of things in his reports and may not even have visited Egypt in person, so he is usually not taken as a realiable source.
The book by Mark Lehner mentioned below contains an excellent overview of the survey and alignment methodology used by the Egyptians to construct their pyramids. There is also a superb overview of the construction techniques and tools. Lehner also recounts the NOVA experiment in building a pyramid using the same labor and tools and the ancient Egyptians.
For more information see, search for information at:
http://en.wikipedia.org
http://www.touregypt.net
Or search Google for "Mark Lehner"
I strongly discourage relying on sources that do not have an obvious relationship to a well-respected scholar, are not related to an educational establishment of some kind, and/or are not subjected to peer review of some kind.
I also recommend looking at the book "The Complete Pyramids" by Mark Lehner.