My longest running part? Far and away my HP LaserJet 4L printer. Purchased in December 1993 for my Twinhead OEM'ed Tandy 486 laptop, this thing has survived college and the required term papers, three relationships, and three roller coaster rides on UPS Ground. I still have it and it works great, not a problem.
Second place goes to two parts I got at the same time:
1) A Matrox 850 meg hard disk drive. I got it with my superfast 486-DX4 100 MHz system way way back in July 1995.

It was my primary Windows 95 HDD for three years, then my SuSE Linux drive until just about 3 weeks ago. It was still running fine when I took it out of my system.
2) The FDD from that system.
(Looking forward to all the parts coming in for my new Athlon 1.33 GHz, just days away...

)