I've owned loads of consoles, these are the ones I have had issues with, memory might be a little fuzzy on some:
PSone - Went through three, first two died due to disc drive wearing out, presumably due to extensive, borderline sad levels of use. I blame FF8, THPS, and GT2.
Dreamcast - The first two I owned, the controller ports shorted out. Apparently this was not an uncommon problem. I also shorted one out myself trying to mod it to play the Japanese version of MvsC2 and Sega GT that I had ordered online. I also wore out the disc drive on a 4th one, again due to massive overuse. I blame Phantasy Star Online, NFL2k1, and Unreal Tournament.
PS2 - I eventually had to replace one due to the DRE, a common problem for PS2's it seemed. Could also chock this up potentially to it just wearing out due to me wearing it out. I blame SOCOM II.
360 - I went through three of these. The first two due, of course, to RROD. lol, I remember being so excited about getting the first "repair" back, I could finally rejoin all my coworkers in our nightly late night Search & Destroy CoD4 marathons. I unpacked it, hooked it up, 10 minutes later it was flashing RROD again. Second "repair" lasted a few days I think. Finally the third console they sent back was actually a new model and never gave me any troubles.
Xbone - My Xbox One died recently and to be honest idk if I am going to pay for the repair or if I am done with MS. I hit up support because one game was making my console lag and would barely load, all other apps and games were just fine. The agent directed me to the Xbone offline diagnostic tool page and basically just told me good luck and that's all the help I got. I followed his instructions and it didn't work. But then, neither did my console. After days of talking with support I was told to try another file system off the page, no dice. I was then told by an agent that I was originally given bad repair support and told the wrong thing and that as a result my console was bricked and MS would be happy to pay for the repair. I sent it in as instructed, then a few days later got an email from someone at the repair center saying they had my unit but no repair order. So I talk to support again and then they say the other agent was wrong, it isn't their fault the unit bricked, and I don't get a free repair. I told them to send it back, that I wouldn't pay to fix their mistake. Someone from escalated support contacted me and she is supposedly trying to work out some sort of courtesy repair. If they honor their word, cool, I will continue to support them over my PS4 since I like the UI and controller more. If not, fuck em, I have a PS4 and will buy a secondary backup PS4 before I'd spend $100+ to fix their mistake.
PS4 - No console issues, but the controller is a hot mess.
By the way, I think the most durable console I have ever owned is the Genesis. Mine was submerged for hours in a flood but as soon as I dried it out I was back to playing NBA Jam just fine.