In Chronological Order:
NES: I think the first NES we got stopped working because we'd always leave games in the cartridge slot and that bends the contacts. We got our first NES in 1989, tried to replace it with a new one in 1991.
Playstation: I couldn't figure out why games were giving me disc read errors (I think it was a venting issue that plagued early units). At the time I thought maybe the lens was dirty, so I tried to clean it with a Q-Tip. That just made things worse. Wal-mart let me exchange it straight across for a Dualshock version for no extra cost and no questions asked two years later.
Dreamcast: I have become one of those people who's Dreamcast is having increasing trouble reading game discs. It mainly only really effects a handful of my library (notably Sonic Adventure 2) but it's still a problem. I have yet to replace it.
Xbox 360: Bought in September 2006, red ringed by December 2006. Microsoft then lost my 360 at their repair center until March 2007. They replaced the console at no extra cost and gave me a free copy of Project Gotham 3. The replacement they gave me was also obviously broken and eventually shit the bed in April 2008, literally two weeks after my new warranty expired. It wasn't even a red ring the second time around, but they ended up giving me 50% off the repair cost (though it should've been free..)
Playstation 2: Same time I bought my 360, I got a refurb PS2 (fat) as I'd never had one before. Around 2009, I started getting Disc Read errors and the controller/memory card ports started dropping connections during games. Replaced it with a refurbished PS2 Slim in 2011.
SNES: Hooked up my old SNES in 2010 to find that
one of the cartridge pins had fallen out (?!) and I have no idea how, why, or when. Yet to be replaced.
Nintendo DS Lite: Eventually succumbed to a bad hinge crack in 2012 and the top screen stopped displaying anything at all.