I really enjoyed reading Decline and Fall of the Roman Empire by Gibbon. I'm sure his ideas are no longer current, but I loved the prose.
I also really liked Toynbee's A Study of History.
What are some other, perhaps less well known, works of history that are considered classics in their own right?
I'm especially interested in the Roman civil wars and early empire period. When I was reading Decline and Fall I found myself really wishing Gibbon had written about that time period as well.
When you use the word "classics" you're going to start bringing the classicists out of the woodwork :)
For 'classics' as in actually written in antiquity, there are several famous sources (some of which Gibbon used himself):
Tacitus Annals, this work goes through year by year from the reign of Tiberius through to the reign of Nero (but we are missing parts). Tacitus is, in many ways, considered one of the fathers of academic history.
Suetonius Lives of the Twelve Caesars. Suetonius starts at Julius Caesar, and works through to Domitian, the last Flavian emperor.
Cassius Dio Roman History, a mammoth history covering the kingdom, republic, and empire, about 1400 years in total.
Livy History of Rome. Guess what this one's about!
I guess they're classical works that are considered historical :P, but if we're looking for information about the Roman world, often all we have to go on is one of the ancient authors (although we usually have a lot of material evidence as well, which helps)
Happy reading!