That depends. Threaded or Threadless?

For most threaded headsets, you'll need a headset wrench of the appropriate size and a big ol' crescent to properly adjust the bearings.
For threadless, if your new fork doesn't have a starfangled nut or similar device in it, they do make tools for inserting starfangled nuts. Not sure how crucial they are. When I buy threadless headsets, I just get ones with "similar devices" so I don't have to worry about it.

They also make special tools for installing crown races, but I've gotten by with careful use of a screwdriver and hammer. Pipe with the proper ID and hammer would probably be better.

All other tools are pretty standard allen wrenches, etc. hacksaw/pipecutter if cutting needed.