Basic Tools for Robots
Screwdriver(s)
I like the kind of screwdrivers with many different heads in the handle. Alternately you can use a set of screwdrivers. Besides a normal screwdriver set you should get a set of smaller jewelry or PC repair screwdrivers. These are flat head and phillips head screwdrivers for screws much smaller then normal carpentry projects.
Wire Cutter & Wire StripperYou can usually find a tool that does both. A cheap simple one is probably fine.
Soldering IronA 25 Watt pencil soldering iron works fine. I don't think you need anything fancy. You may want a little suction bulb to suck out solder and a little metal pick to clear the solder in certain situations. You also need a damp rag to wipe the iron, a small clamp stand to hold pieces being soldered.
Needle Nose Pliers
You will use this for many things, but particularly for crimping wires and holding small parts while soldering.
VOM (Volts Ohm Meter) or Multitester
I don't like getting anything too fancy for this. The main uses for me are to measure voltage (is the power getting through? is the battery dead?) or resistance (is there a connection?). I used to use an analog one, but even at Radio Shack they all seem digital now. I have broken a few, so I do not recommend spending much on one, at least until you know what you want.
If you are making a robot that is less then 6 lbs / 4 Kg, you can probably do all the cutting, drilling, and grinding that you need to do with a dremel. Dremels are incredibly versatile. I recommend getting the type with a cord. They last forever and are always useful.
Alligator ClipsA couple of short, flexible wires with alligator clips on both ends are very useful for testing circuits.
Glue Gun
I actually learned about glue guns from doing crafts with my kids. They are really cheap, easy to use, and amazingly versatile. They do not make the strongest connection but they can get almost any two things to stick together quickly. That can be useful for fastening a sensor to a chassis, or gluing a bolt to prevent it from unscrewing.
Tin Snips
You do awesome things with thin sheet steel or thin sheet aluminum. Even though they are strong, you can cut and drill them with power tools. Tin snips are the easiest way to cut up a piece of sheet metal.
Table / Workspace
When I first started building robots I lived in a tiny place with no workspace. I got a little fold out Black & Decker Workmate table. Now I have a much bigger house but I still use that same fold out table. You need a sturdy table that you clamp pieces too and that you can afford to scuff or spill glue on. It's the kind of thing you may overlook but it is very important.
As you develop software for your robot or test it you may need a way to hang or hold it so that the wheels or legs can move rotate without moving the robot. To test your robot you may need to be able to run it plugged in. Robot have a tendency to engage unintentionally, so it can be very helpful to have a stand that will prevent it from jumping off a table or pulling out a cable.
Clamps
You can probably use a larger clamp to hold pieces of lexan, metal, or wood for drilling or cutting. You can also use a little clamp or stand to hold boards while you solder them. You also need some material like cloth or soft wood to keep the clamped material from scratching or cracking while you cut or drill it.
Power ToolsIf you make something bigger you may want a cordless drill, a scroll saw, chop saw, drill press. I really recommend building smaller projects and then seeing what you need before getting into this. I use a drill press, a power drill, a dremel, and a jigsaw. I am thinking about getting a bandsaw.