Min Min is one of my personal favorite fighters in Arms. In the story she is part of Ramen royalty (WTF is that anyway?) and she is a big parody almost of Ramen eating in general.
I like using her in the game because she's small and quick, very agile, and works against most foes in battle.
Her special ability to kick in mid-air. It's actually not as useful at knocking blows away as it is about becoming very difficult for the other play to hit. I often use it to run the clock down when I'm ahead in health points on the bar.
Now she technically isn't my favorite in the game but she's close to the top.