King of Fighters 13 is an excellent fighting game from Atlus. The character designs are very interesting and the game is rewarding and fun. MLG (Major League Gaming) is going to host a tournament for this. It's not a big name like Street Fighter but it's worth looking into.
Here is some high level play so you can get an idea of what it's like (skip to 1:35):
[youtube]http://www.youtube.com/watch?v=hutxjlT-ems[/youtube]
Fighting games are kind of my thing (my special interest) and I play them competitively. But even if you just mess around it's still a good time. You can get this game cheap, I got it for $30.
I love the art style in Blazblue but I find the game very dry at competitive levels of play, for reasons I won't get into right now, but if it looks interesting to you go for it. The online for it is GREAT almost no lag whatsoever. There is a big emphasis on huge combos, unlike Street Fighter, in which even the longest combos rarely go over 8-10 hits.
I play Street Fighter IV also and I think it's a bit slow-paced, otherwise pretty good. It's VERY balanced with the newest patch. I like the emphasis on outthinking your opponent too, and spacing is important in this game.
I don't play Tekken but I'm friends with one of the best Tekken players in the world. That game is very complex to do the advanced stuff, but it's actually easier than the other games mentioned to get the basic combos down. Spacing is not a big deal in Tekken it is more about making quick reads, thinking on your feet, and knowing when to attack and when to defend in all situations.
Virtua Fighter is even more complex than Tekken, however, it is an incredibly solid game. I don't think it's very fun but that's just opinion, you may think the complete opposite.
So basically it's all about taste...I can't tell you which fighting game you would probably like the most it's all about what characters you like best, how fast paced you want the game to be, etc.