Shooters, old school 16 bit ones are my favourite's, my absolute favourite genre and time frame (i was in my 20's and at the peak of my gaming powers).
I do like the modern cave variety as well and some of them look absolutely stunning, it's like being caught up in the middle of a multicoloured firework display, really pleasing on the eye.
I also find some of the modern one's easier because of the smaller hit box, but that's not to say that they're a pushover, far from it actually.
Fighting games i suck at big time and i've alway's had very little interst in them because of this, i'm a button bashing spaz who rely's on pot luck to get anywhere and fail's epically, i would go as far as saying i'm probably one of the worse fighting game player's on ng.com. I do however see the appeal if you can pull of the special's and combo's.