FreeCiv covers civ 1 and 2 more or less.
Personally, I didn't play much of 2 or 3, so I don't have strong feelings either way.
UnCiv covers civ 5 as well so I think there's a place for something in between
especially since openciv3 aims to fix some of civ 3's shortcomings
Freeciv's point of interest is that it's not trying to exactly replicate any one of the original Civs: it has its default ruleset plus others that are closer to the original games, but it's very easy to make your own.