Too many. However, I'll mention important campaigns with a few stand-alone battles (however, some campaigns are named battles although they're not battles) and pick the important battles out the campaigns, if any.
1) Invasion of Poland (1939)
2) Phoney War (1939-1940)
3) Winter War (1939-1940)
4) Battle of the Atlantic (1939-1945)
5) Operation Weserübung (1940)
6) Battle of France (1940)
7) Battle of Britain (1940)
8) Western Desert Campaign (1940-1943)
9) Italian conquest of British Somaliland (1940)
10) Occupation of the Baltic States (1940-1991; two occupiers; two wars)
11) Soviet Occupation of Bessarabia and Northern Bukovina (1940)
12) Invasion of French Indochina (1940)
13) Greco-Italian War (1940-1941)
14) Operation Compass (1940-1941)
15) East Africa Campaign (1940-1941)
16) Invasion of Yugoslavia (1941)
17) Yugoslav Front (1941-1945)
18) Battle of Greece (1941)
19) Battle of Crete (1941)
20) Operation Barbarossa (1941)
21) Continuation War (1941-1944)
22) Middle East Campaign (no battles among allied v. axis fought there)
23) Battle of Kiev (1941)
24) Siege of Leningrad (1941-1944)
25) Battle of Moscow (1941-1942)
26) Siege of Sevastopol (1941-1942)
27) Attack on Pearl Harbor (1941)
28) Battle of the Coral Sea (1942)
29) Battle of Midway (1942)
30) Battle of Stalingrad (1942-1943)
31) Second Battle of El Alamein (1942)
32) Operation Torch (1942)
33) Guadalcanal Campaign (1942-1943)
34) Tunisia Campaign (1942-1943)
35) Battle of Kursk (1943)
36) Battle of Smolensk (1943)
37) Solomon Islands Campaign (1942-1945)
38) Invasion of Sicily (1943)
39) Lower Dnieper Offensive (1943)
40) Invasion of Italy (1943)
41) Gilbert and Marshall Islands campaign (1943-1944)
42) Battle of Monte Cassino (1944)
43) Operation Shingle (1944)
44) Battle of Narva (1944)
45) Invasion of Normandy (1944)
46) Mariana and Palau Islands campaign (1944)
47) Operation Bagration (1944)
48) Lvov–Sandomierz Offensive (1944)
49) Warsaw Uprising (1944)
50) Jassy–Kishinev Offensive (1944)
51) Belgrade Offensive (1944)
52) Liberation of Paris (1944)
53) Gothic Line (1944)
54) Operation Market Garden (1944)
55) Operation Crossbow (1943-1945)
56) Operation Pointblank (1943-1944)
57) Lapland War (1944-1945)
58) Budapest Offensive (1944-1945)
59) Battle of Leyte Gulf (1944)
60) Battle of the Bulge (1944-1945)
61) Vistula–Oder Offensive (1945)
62) Battle of Iwo Jima (1945)
63) Battle of Okinawa (1945)
64) Spring 1945 offensive in Italy (1945)
65) Battle of Berlin (1945)
66) Prague Offensive (1945)
67) Siege of Budapest (1944-1945)
68) Soviet invasion of Manchuria (1945)
69) Battle of Manila (1945)
70) Atomic bombings of Hiroshima and Nagasaki (1945)