Civ III was the first civ game I played. It would still be my favorite if I had not discovered that Civ IV has vastly superior mods. Because of Civ IV mods I haven't bothered with Civ III in years. I generally only play my own modmods of FfH, although recently I've been playing more Dune Wars.
I bought Civ II really cheap the year before Civ IV came out (actually I think it was one of several cheap computer games mom got me for Christmas that year). I never actually finished a game though.
I bought Civ V and at least started a couple dozen games, but never really got into it. I found it more annoying than fun. It seems to increase the bad kinds of micromanagement while decreasing its usefulness. I really hate not being able to end my turns early without always giving orders to all of my units and cities. Also, the last time I looked the selection of mods was not yet very impressive.
I haven't played any Civ in the past week, because my laptop's AC adapter stopped working. I found and ordered a cheap replacement online, but probably won't arrive for another week. In the meantime I have reclaimed my old laptop. (My dad was using it for a while, but since he returned and moved his desktop home from the office he has no use for it.) I deleted all the games (except the basic ones like solitaire of course) from it when I got my new laptop about 19 months ago, and don't want to bother reinstalling them again. (This week I've mostly just played Free Cell.) It still works fine for basic internet use, but the screen sucks. The brightest it will go is still pretty dim and there are about 140 one pixel wide vertical lines of random colors obscuring much of the screen.