I’d tried the Dolphin emulator a while back, but wasn’t able to get it configured to run somewhat smoothly until recently. I finally have some decent screenshots of what Nintendo Wii games could look like in 720p (click on the images for the full image).
New Super Mario Bros. Wii
I was able to get NSMB Wii running at a somewhat consistent rate, usually around 40-50 fps. NSMB appears to be a good game to start with, since it is supposed to run pretty well on most any system with at least a 2 Ghz processor.
I tried a few other games, but didn’t have much success. Little King’s Story had graphical glitches galore, Super Mario Galaxy looked fantastic, but ran slow (i.e. 5-15 fps), and Mario Kart Wii did run, but had a few glitches and was a sub-par frame rate for a racing game (20-30 fps).