Add me to those on here that have said NES and Dreamcast.
My NES was removed from my possession in the mid 90's, but it had all sorts of issues. I would have to stack a 2nd cartridge into it to hold the one I was trying to play in place, the connectors were going, etc. I have no doubt that the NES would not have survived my various moves I've had over my life.
My Dreamcast also is in bad shape. It won't read the vast majority of my games, MvC2 is the only game I have that consistently reads, and it has issues, skips, etc.
On the flip side, my SNES and Saturn are tough as nails. The controllers have held up extremely well over the years, and they all have gotten a lot of play. My N64 and Dreamcast controllers have not aged well at all, and replacing them is actually pretty high on my priorities list.
While many people have said they've had bad luck with PS2s, I'm on my original and it doesn't have any problems at all. The controllers are for the most part durable, but one of my 4 controllers has a bad analog stick.
I think that the SNES is the toughest system I have overall, with the PS2 or the Saturn for CD based systems.
I have actually been really disappointed with my DC overall. When I was reading the Critic's system reviews, he really speaks highly of the system, but I find it to be my least played, most difficult system. Now, my game selection isn't fantastic, but I have a ton of "the hits." Virtua Tennis, Crazy Taxi, Power Stone 2, Soul Caliber, MvC2, etc... and I still play it the absolute least of all my systems. I probably haven't found the right game yet to get me hooked... but with its reliability issues I view the system overall poorly.
I really like my Saturn though, which the Critic grades much more harshly overall than the Dreamcast. It's really interesting to see the differences in opinions brought on by this site. So many different types of gamers.