Console-wise... I still have my very first console-- a Super Nintendo that I got back in Christmas of '93, give or take a year. It's sadly succumbed to the "nicotinitis" (that awful discoloration) that plagues most of these, but it still works like a charm! Right now, it's collecting a bit of dust no thanks to my Wii and 3DS, but that'll change once October's eve approaches for my yearly non-stop run of Zombies Ate My Neighbors.
I still play my Gamecube on a semi-regular basis, mainly its GameBoy Player. It's Platinum and has Zelda: Twilight Princess decals on the front and disc cover. I used to own a Nintendo 64, but sadly it was given away to some cousin I don't even remember. The only remnants of it I have is my Voice-Recognition Unit... sans microphone.
On to portables... I have an old green GameBoy Color with a broken speaker. The only way to hear sound is to plug in some headphones. Otherwise, it still works. There's a first-gen glacier GameBoy Advance sitting in a box, which works fine except its Power switch is a little funky. One wrong nudge and the system shuts off. Also, like many GBAs before it, it's missing its freaking battery cover. Thankfully, I got it for free so it's not a big deal.
I used to have a red GBA SP, but I gave that to another cousin as a birthday gift. I also had an original blue DS, which I gave to my sister so she could have something to entertain herself with during her breaks from work. It still works wonderfully.
Lastly, I have a red DS Lite that's practically falling apart no thanks to yet even more little cousins. It's had its touch screen replaced twice, and now sports a broken left speaker, a wonky headphone port, and a top screen that doesn't display colors properly near the top. Regardless, it's still alive and kickin', but I haven't lent it to anyone else ever since the second touch screen surgery. After witnessing that thing's fate first-hand, I swore that I wouldn't lend my 3DS to anyone.