New to the Civilization Series

Civ 5 is great with the basic but if you want all the factions and have the money go for it

Civ3 and 4 are arguably the best in the series. Civ5 might be all shine, but does not have the depth of the others. Still, Civ5 is a good entry point. But if you feel that you want a challenge, go for 3 and 4.

Civ5, because it's simpler and easier.

civ 2 was the best

You should get Civilization 5 as it's the easiest to get into, it's really simple and streamlined. I heard that Civilization III is pretty bad and IV is the best from the series (hate comments incoming).

You should also get the complete version because it's cheap and it gives a lot of additional functions to the game that will greatly expand the possibilities and further enhance the game. (like religion, trade routes etc)

Civilization 4 complete is the best the series has produced the recent years. It is better than 3 or 5 by a clear margin.

Civ IV (complete) was indeed the pinnacle. Civ III is soulless compared to IV. V became nice after the expansions, but still... IV remains to be the best so far (though it could use some aspects of V).

EDIT: I and II were really great in their time too. But I doubt you'd like to go back that far. Btw, I still play the original Colonization (1994) and Alpha Centauri (1999), which are both incredibly successful variations, which should have overshadowed the main series.

I don't know, but Civilization V is always on the "Top 10 games by current player count" on Steam: http://store.steampowered.com/stats/

Civ 4 is better than Civ5, but Civ5 is still loads of fun, especially if you play it with your friends (the AI is ridiculously crap at trading)

The new one seems pretty snazzy. Seeing how you are out there exploring other "worlds" with the dangers it may hold. :B

Civ V is good with the expansions. Get both Civ V + expansions and Civ IV Complete.

I played a ton of 2 through 5, covering most expansions (and later "DLC"). 2 was a great one to get into it, but by now it's so dated I wouldn't recommend that to anyone save for nostalgia-reasons, not fitting the "new to the series" people. 3 Wasn't bad per se, good thing to play back then but... well, when there is a 'but' at the end of the line, you probably know where that's going.

Civ IV then, the-game-I-keep-buying... bought it when it was new, bought it again in a complete pack, bought it again during a steam sale just to have it in my library there. The game is an extraordinary example of "a solid game" where every aspect of the game just somehow 'works' for it. Takes some time to learn exactly which resources you want to focus on, which starting positions are good and such, but once you get the hang of that and start playing the game itself, near perfect. If you get it, get a pack that includes the "Warlords" and "Beyond the Sword" expansions, both adding interesting features and systems to the game. Some good mods out there to, if you're into that sort of thing.

And then there's Civ V. This one is a little different, but it's a great game regardless. Like above, get the complete pack, so you're up to date on the two main expansions and the loads of DLC. This one comes with steam workshop integration and there are a LOT of mods out there adding more civs, more units, more systems, more anyting, and a few good ones that change the core game mechanics. That, and they're mostly very easy (one-click easy) to install and play.

So, in short: I Recommend 4 if you're into things that are a bit tough to get into. 5 is definitely a good entry-point to get into stuff a lot smoother, and still requires a deep enough skillset to stay interesting. Workshop is great on the latter too. Regardless either one will keep you entertained for hundreds of hours, especially if you get the complete pack.

Note: For all titles I played almost exclusively singleplayer, so if multi is your thing, find someone who has experience there.

Update 2 seconds after posting:

WARNING!!! Playing Civilization (any one of them) is known to be incredibly addictive, you WILL lose track of time, you WILL want to play just "one more turn" before going to bed and you WILL find yourself at 7 in the morning still playing it. You have been warned!

Civ V is the perfect entry point IMO. IV has stacks of death and III is just plain old (no matter what they say about the game, its age is reflected in the user experience).

The Complete Edition gets my vote.

My favorite entry in the series is III, but I think Civ V would be the best game for someone who is new to the franchise.