I'd take them all, they give new views and strategies to the game, and it's cool to get different adversaries too.
The Mongols, which are the one we got free are actually my least favorite, too straightforward I guess.
Inca and Spanish are my favorites, both very unique, and it's cool to make a colonial Empire with Spain. Spain is fun also for later era starts if you like those once in a while.
Inca is both very strong and interesting, good for production powerhouse civ, it's nice to use hills and mountains to new advantages.
Haven't tried Babylon that much but it has it's fans. Bowmen are very good, an underrated UU!
Polynesia is another one people dig a lot, the embarked bonus is good but I haven't found a good synergy with their UA + maori warriors + moai statues... Great thememusic and boat graphs..
Just finished a game with Denmark (lost to Babylon!) and I like them, I played a game where I pillaged some weak civs to stone age, I wasn't that popular Civ with other leaders but some civs forgave my sins thankfully.
Berserkers are great looking and great marines, but the july patch downgrades them a bit, but it's ok.
Ski infantry is ok I guess, but it's nice to have a rifleman UU.
Seriously, get them all! Save a few bucks from your expensive fair trade coffee and buy the cheapest coffee you find at your cheap-mart. You have already enough cash for Denmark!
Repeat with other "luxury resources" and you'll get them all..