To include this gen's systems is a mistake. You really need to be able to look at the generation as a whole in order to determine a particular systems' greatness. I also feel that handhelds should be separate.
1. SNES - the controller set the standard with shoulder buttons and the basic design can be found in almost every controller to follow. Incredible game library.
2. NES - without it we probably wouldn't be gaming. NES single handedly saved the home console
3. PS2 - While there aren't many games that i personally enjoy, I can't deny the positive impact it had on the gaming community. It greatly expanded the market.
4. N64 - Innovations like the analog stick, rumble pack, and trigger button, as well as having most of the best games of all time, LoZ OoT, Mario 64, Goldeneye etc... Would be higher if it were able to reach more people and expand the market more
5. PS1 - Was the system that proved that optical media was the way of the future. Also helped to expand the market greatly
6. Genesis - Brought many great arcade classics home. Also was the home of the greatest Sonic games ever.
7. Gamecube - Most comfortable controller or all time. Had many incredible games SSBM, SMS, LoZ WW, Metroid, etc..
8. Atari 2600 - Had the longest life of any system, had all the classic games we all look back on fondly today. Would have been higher if it didn't lead to the crash of video games by allowing things like ET to exist
9. XBox - Brought many of the PC gamers to the world of console gaming. Proved that online gaming was the way of the future.
10. Dreamcast - First real attempt at online gaming with Sega Net. Had some great innovations like the VMU which had a lot of potential. Showed that a system can launch with a good line up of games. Would be higher if it lasted the whole generation.
Handhelds
1. Gameboy / GBC - Without it, handheld gaming wouldn't be as we know it today.
2. GBA - Everything you could have hoped for as the next generation Gameboy. Great games, very portable, great battery life, BACKLIGHT!! (SP and micro versions).
3. Game Gear - Had some awesome games and some amazing visuals. Battery life was appalling and was not exactly portable.
4. Nomad - Played all of your loved genesis games. Appalling battery life. Clunky and definately not portable.
5. Virtual Boy - yea i said it! It was an awesome idea and mario tennis was really cool. Eye strain and the fact that it is not portable at all makes it low on this list.