Pokerstars is the biggest, personally I find it has the cleanest interface and best variety of games, especially at low stakes if you're just starting out.
FullTilt is the other monster site, a lot of the internet-pros play there as you can get "rakeback" depending how you signup. I wouldn't worry about that now though, FT is a great site too but I find it easier to bust out on.
Ipoker is the third biggest network, there's a variety of "skins" for it, Titan poker being the most popular. Unlike the other two it doesn't allow US players but there's plenty of Euro donks on it. Tourneys there tend not to be quite as enormous as on PS and FT but still a lot of activity, its a pretty good site to start out on.
I'd really recommend one of those 3 above the rest.
These days you don't get the same sort of signup bonuses to poker sites people once did, usually they'll just give you a 100% bonus on your first deposit but you earn that back as you play and earn "points", not in one go. From sloveniankopite's signature on here, this is a decent offer for Titan poker -
http://pokernetonline.com/index.php?uid=MTkx. Ones for Full tillt or Pokerstars are easy enough to find with a quick google.