I have two favourite fighting series and one game, I can't really choose a favourite out of all of them either...
The first one is Street Fighter, I loved playing this with my cousin when I went around his on most week ends, it's a fun fighting game an unlike most games that you find now again, was actually challenging (well, it was for me when I played it, I must have been about 7 or 8. It's a great game that has several cool characters and I find that it has great reply value.
The next series is Super Smash Bros., I don't know anyone that doesn't actually like this game, it's fun for most people to play that are generally interested in gaming, it's a great game to play when you are at a party or someone's house with several friends, it's even better now that there is the new Rotation system on the Wii that allows for groups of 5 or more play the game with everyone getting a turn. The Tournament system is also very fun to play, it's probably one of the better mode's to play on when lots of people are playing.
The final game that I enjoy playing is Teenage Mutant Ninja Turtles, I believe the game I'm thinking of is the arcade version, this is once again a game I used to play on at my cousins house, I loved this game since I first started playing it and it also has it's share of funny moments (like when you try and walk over a hole in the ground and fall down it :xd
. So there they are, my favourite fighting games, if I had to choose a favourite out of them it's probably one of the latter two as I can still play them by myself where as the former one gets a bit boring without your friends, when you are playing with friends in when that game really starts to excel.