One game on here I did not realise was actually a good game - I didn't play it for that reason but now what might I have been missing?!
Luigi's Mansion was good? I will definitely try to get my hands on it or play an emulated version.

Super Smash Bros!
It took me ages to try this franchise because I've never been one for fighting types or shooter type games, but since it was available as a free download on my Wii one day I tried it and loved it.
I hadn't played Melee though, looks pretty sweet!

If we are talking about Game Cube games then we can not fail to mention ANIMAL CROSSING! The original for Game Cube is probably still one of the best versions of the franchise!