Uses for an obsolete 286

• Install a bare-bones linux distro and set up a primal gateway.
  If that fails, install windows 98 and set up Connection Sharing. (To get over the slowness factor, imagine it's XP running on your Pentium III.)
• Write a basic database interface and give it to a small business to keep track of inventory.
• Set up a Telnet BBS
• Set up a Dialup BBS
• Donate it to the Red Cross or your favorite charity organization. Some Schools out there do run DOS and DOS browsers and would love to use it.
• Get a TV out card and play Commander Keen and Wolfenstein. Can we say "Retro night"?
• Find the spare change around your house, go to the flea market and set up the dream system of yesterdecade. =)

• Build an elevator at one of the biggest elevator manufacturers in the world

A bunch of elevators in Helsinki run on 286s. Yes, really. One of them where I work has a 286 that crashes all the time, seemingly due to a corrupt boot floppy (and it's probably one of the really floppy, ancient ones). It's the machine that indicates which floor the elevator is on and where it's going to stop next. Luckily the movement itself seems to be controlled by another system. The BIOS is dated 1991.