In MUGEN - As long as they play well and don't glitch, I'm happy.
In Fighting Games - Visually appealing, and must offer a challenge to learn.
Spoiler: "Challenge" (click to see content)
When my crew started hitting SF3:3S, everybody was alienated by the new characters, and nobody wanted to venture to try new stuff, so it was mostly SHOTO fights (BORING AS SHIT). I then challenged them to ban shotos from out sessions, and main 2 characters completely alien to them, and we couldn't repeat.
I picked Urien + Hugo, both having SUPER SLOW basics that got outmatched by pretty much everybody's speed. It took me 3 weeks of frustration for getting my ass handed to me, until I finally came up with some Mix-Up strategies using Urien's Overheads ... and by the time I mastered him, I was champ among my buds.
Same when SF4 came out, I wanted Rose. She may have the moveset of a shoto, but it works completely different (i.e. LESS EFFECTIVE). You can mash DP, but it ain't going to take you out of any unfavorable situations. Her fireball is slower than a Hadouken. I had to master her Foosie Game (she has mad range) and her limited comboability to start getting some respect.
For Ultra, I will make Poison work, no matter what.