The ones that I chose were the NES, Super NES, N64, GBA, DS, and Wii. Below are reasons..
NES- Arcade gaming finally started coming home with the NES, and it was Nintendo's first system. Whee!!
Snes- A step forward in art and design. Characters start to stand out more, and backgrounds are more colorful.
N64- First really succesful 3D system*. Super Mario 64 defined what a 3D game should be, and many of today's games still seem to copy it.
GBA- 4 players can play from one game pak, it can communicate with the GC, and play your pre-existing library of GB games. Whoo-hoo!
DS- Touch screen controls are fun to use, and it seems this Nintendo's second system to use the initials DS (the Famicom Disk System being the first. Is Nintendo going to go back and start reusing old initials for newer systems? Is there going to be another system with the initals VB??
Wii- Motion sensing controls! Wario Ware knows how you're holding the Wii-mote, you actually swing a sword along side Link, and most of the games recognize your Miis, so if you have a Plaza full, be prepared to look for some of your favorites.
*I realise the Saturn was the first 3D system, but not many people that I knew even knew it existed until long after the N64 had come out.
EDIT: Whoops! The Saturn came before the Dreamcast, so I am wrong. (-_-;)