Call of Duty 4 and MW2 taught me the phrases "Oscar Mike" and "Danger Close" and the meaning of "NEST"
Rome Total War taught me the most basic things about ancient Rome and Greece, but it actually did me a disservice; in order to portray the Roman civil wars, they literally make Rome into three separate factions---it would be as if a strategy game depicting America had it divided between Republican America and Democratic America, subject to major electoral results. I actually thought that Romans who wore red were a part of the House of Julii, and those in dark blue were a part of the House of Scipii (which I learned later is a butchering that should be Scipiones)
Mods for RTW, particularly Europa Barbarorum, re-taught me things about Greece and Rome, including proper Latin/Greek/Eastern/Celtic/Germanic/Semitic names for certain towns, cities, military units, and people. It even has a "This Year in History" popup every year for 272 BC through 200 BC or so that provides a bunch of details of what was happening in real history that year that has taught me a whole lot more than any but the most dense and detailed of accounts.