I can't name my top 10 but I will give you my top 5. There are many systems that were great but were simply out of my reach since they either didn't do that well in the U.S. and didn't produce the best games. Such systems are: Saturn and Turbo Grafx-16/Duo. The Saturn in Japan had some amazing games that would easily have destroyed the Playstation in terms of games, but I am not able to experience such games since I am not a hardcore collector and am not willing to spend that much on import games. Same goes with Turbo Grafx-16/Duo which had great Japanese games but weak U.S. games due to poor sales. However, here are my top 5 systems that I am able to afford or play, and are common enough in terms of great games:

Genesis
NES
Playstation
Dreamcast
Neo Geo (arcade)