They call Herodotus "father of history" for a reason. "The Histories" would probably be a good start. I cannot recommend a translator offhand.
Thucydides' "History of the Pelopennesian War" is also very much worth a look. Again, I'm not sure which translator would be best.
Edward Gibbon is way to important to not mention. He wrote The book on The empire, what can I say? "Decline and Fall of the Roman Empire"
In the roman vein, Suetonius' "The Twelve Caesars" is an interesting one. Roman emperial decadence was pretty cool indeed.
MacKay's "Extraordinary Popular Delusions and the Madness of Crowds" is absolutely delightful fun, with the hilarious details of a variety of periods of remarkable human folly.
Barzun's "From Dawn To Decadence" is really wonderful stuff. Practically every page just drips with fascinating things, most of which you'll want to end up looking up as well.
Darnton's "The Forbidden Bestsellers of Pre-Revolutionary France" and "The Great Cat Massacre: And Other Episodes in French Cultural History" are both wildly entertaining looks at the enlightenment.
Hanson's "Carnage and Culture" is definitely worth a look if you fancy military history at all. Basically the about western culture, as it fights, with numerous examples. Also makes a nice counterpart to "Guns Germs and Steel" which I think someone has already mentioned.
Foucault's "Discipline and Punish"(rather more historical than it sounds) and "Madness and Civilization" are quite interesting, if perhaps a bit more philosophical than strictly historical.
"The Book of Deeds of James I of Aragon" is interesting history in its own right(if you fancy the place and the period) but has also, if I remember correctly, the distinction of being the first autobiography in occidental history.
Sorry about the somewhat disorganized list, I'm a bit scattershot about this sort of thing.
About the issues of best translator, have a chat with a reference librarian. The'll know, or know someone who does. Have a chat with a reference librarian anyway, you pretty much cannot lose, when talking to someone whose job is basically to know things about knowing things.