Let's see, I could talk all day about this. Having played everything from Street Fighter 1 (yes the original before the one on the SNES), to SSBM, there are a lot of good points about each fighting game series.
Street Fighter for me, is classic and one of the best series. Mainly, these games are about knowing the combos (well, this is true for most fighting games, but especially so for SF), especially when it comes to Super Combos. Best of the series for me, has to be Street Fighter Alpha 3.
Mortal Kombat. It was the big rival to Street Fighter back in the day, but now it's somewhat less popular. Nevertheless, it's still a favourite of mine. They can make it bloodier, gorier and simple as possible. Overall, MK series is easy to pick up, just as easy to master. It's good for fighting game newbies but not much else, but still good for a laugh. Fave in the series has to be MK Trilogy.
Killer Instinct. Anyone remember this one? It's an old clone of MK really, just as simple and bloody, but still lots of fun.
DOA. I've only played a DOA game once, and quite frankly, I think the series sucks. The combo system seems to be more about button bashing than anything (one of the reasons why I've gone off Tekken).
Tekken: Tekken 1, yes! Tekken 2, yes! Tekken 3 and onwards, why? They changed the entire game engine between 2 and 3, making it easier for the newbie button basher to come in, pick up someone cheap like Eddie, and just bash the buttons and win. It's far too easy to link combos with Eddie and similar characters (Hwoarang is another one). For me, Tekken 2 is the best in the series, and any after that just should not exist.
Soul Blade/Calibur: Called Soul Edge in other countries, I first got into Soul Blade when I realised there was a weapon based fighting game (I had heard of the Toshinden series as well, but they quite frankly suck, I had a demo of one of the games). Then Soul Calibur came out, and they'd stuck my fave character from Tekken in there, Yoshimitsu. Tis a cracking series, especially after playing SC 2 with Link :-)
Super Smash Bros (Melee) - This is perhaps the most captivating fighting game I've ever played. With most fighting games, I get quickly bored (cos there's little to do after unlocking every character). With Melee especially, there's still tons to do, and the challenges will keep even the best gamer occupied for months on end. I know I've owned the game over a year now, and I'm only coming up to completing the game fully (current trophy total 286 out of 290). Also, it's a hail back to some of the best classic games from the NES era of Nintendo, and with me being a very old gamer, I can't resist the charm.
Anyway, this is just my coupla coins