If I were forced at gunpoint--hey, it could happen--to pick my favorite 8-bit Super Mario Bros. game, I'd probably go with Super Mario Bros. 2.
And if the gunman--or gunwoman--made me choose a favorite character from said game? I'd point to Princess Peach (aka Princess Toadstool).
As such, it shouldn't be much of a shock to hear me say (see me write?) that I'm a big fan of the following piece of art, produced by deviantartist pluckylump.
See also: 'Catch the Squirrel' and '10048'