I like games for the variety.
Let's look down the list of my favorites (not very long).
SSB
The series that started this community.
This is about as unique and awesome as it gets.
You have your favorite characters from animes and games fighting each other.
I don't see how you couldn't smile at something like this.
I mean, the concept of having Mario against Kirby is really cool.
Touhou
I don't even have any of the games, but it rocks anyway.
SHMUPS are awesome enough (I prefer dodging bullets rather than shooting down planes).
But the second someone introduces an actual STORYLINE and anime characters to go with it, I would say that's something special.
Not only do you play as people, dodge bullets, and shoot down various other beings, but it makes you THINK.
I love puzzles, but hate puzzle games.
But when it's a "Figure it out or flippin' DIE" situation, I like them.
This is the case with Touhou.
It also tests your hand-to-eye coordination (As does every game), but more than many other games.
You must figure out how to dodge the spellcard (aka bullets) and you have to figure out how to kill the boss at the same time.
I'm going to stop here.
But basically, I like them because they're unique.
Super Smash Brothers is quite competitive, has popular anime and OTHER video game characters, and throws in nametags and colors.
It defines who you are, if you look at it.
I like the Christmas colors of Brawl (green n' red), and I have a very cool( I say green and minty), yet aggressive playstyle (there goes the red).
You see?
Touhou is just awesome.
Tells an interesting story, and you get to shoot down anime characters, while dodging complex patterns of bullets, aka spell cards.
Sorry for the mini WOT (Wall of Text, more like Lego Fortress of Text in this case).