This article is from the Car Audio FAQ, by Ian D. Bjorhovde (firstname.lastname@example.org) with numerous contributions by others.
Make sure you get some that can withstand extreme temperature
*Wire cutters/strippers and crimpers*
Get a big pair with stripper holes precut for individual wire
Makes taking dash and rear deck speakers out a lot easier.
*Multiple size screwdrivers, both flathead and Phillips.*
Magnetic screwdrivers can be a big help when trying to get screws
into (or out of) tight spaces.
*Various wrenches, pliers, and socket sets*
The specific sizes you need will depend on your vehicle.
*Metal drill and saw*
You'll need these if you need to modify your vehicle for new
speaker cutouts or to accommodate a new head unit.
*Hot glue gun*
Good for putting carpeting or door panel trim back in place after
Helps for detailed modifications of door panels or carpeting,
especially when installing new speakers.
(see Section 2.3).
Makes excellent connections, but can be messy if not careful.
*Shrink wrap or flex tubing*
Good for protecting wire, especially in the engine compartment.
Helps to diagnose installations.
Screws, nuts, bolts, connectors, etc.
*Fuse puller and extra fuses.*
In addition to the fuses for your stereo system, check your car's
fusebox to find the various sizes you'll need. Also, you can use
needle-nosed pliers to pull fuses.
Helps to tuck wire away in otherwise exposed areas.
*Small light source*
A flashlight will do - you just want something that you can poke
around the innards of your car with.