Since it seems to be the popular thing to do in this thread, I'm going to make a list of my favorites.
1.) SMB3 - perfect controls.. absolutely superb level design and power-ups to play with
2.) SM64 - Mario and 3D are quite a pair, also so many wow moments. Possibly the best launch title ever.
3.) SMG - Gravity physics, complimented by IR controls and a mesh of 2D and 3D. Sign me up.
4.) SMB - As iconic as it is addictive, the game that started this Mario Madness and I wouldn't have it any other way.
5.) SMRPG - A different direction for the plumber but one well worth experiencing. Quirky characters and a journey that rivals other JRPG out there.
6.) MK64 - The first modern Mario Kart. A GP and battle mode that's up there with the best of the genre.
7.) M&L:PiT - A tale of 2 brothers, or maybe four. You decide. Still one of the best RPG's otu there.
8.) MT - Camelot, you may have created the best GBC Mario game ever. Addictive story mode and challenges.
9.) SMS - Isle Delfino may be a great vacation spot but It's business as usual with 3D platforming bliss.
10.) MKWii - Mario Kart redefined. A fantastic online mode with brilliant tracks to be driven and beat through time and time again.
This list was incredibly hard to make.