Didn't we have a thread on this earlier this year?
This is what I need to do 95% of working with a desktop computer.
#2 Phillips screwdriver, long and magnetic
This is the actual screwdriver that I like to use, from the actual source. It is cheap and the extra length is really nice to have when you are trying to reach into the case.
These are handy to have but not essential.
4" magnetic parts tray to hold all loose screws - essential when working on notebooks
assorted cable ties for tidying up cables
diagonal cutters for the cable ties
Pliers and small (5mm?) nutdrivers are useful for restoring the screws on graphics cards that people over-tighten and get stuck on their cables. Nutdrivers also help with motherboard trays.
Size #0 and #00 precision screwdrivers can be handy for working with notebooks or disassembling graphics cards. This is something that IMO you can't go too cheap on, because while with other tools the cheap stuff is often functional enough, I've seen too many cheap precision screwdrivers strip out, or the handles fall apart (srsly wtf) or the tip not grip. Also, I like them to have plastic handles because the ones with super thin metal handles can be tough to turn on tight screws even though they are knurled.
Compressed air is handy for cleaning, as are small brushes.