Hammer A 16-oz. curved-claw nail hammer is your best bet. A rubber grip handle is more comfortable to use for long periods of time.
Saw A cross-cut hand saw will handle most things. There are some short ones that will fit in the average tool box.
Stapler A small, stapler that will also hold small brads can be very handy.
Screwdrivers A small basic set that contains both standard flat blades as well as Phillips heads will tackle most jobs. There are some pretty neat combination drivers that include a variety of blades that all fit on one main handle.
Tape Don't forget the incredible duct tape, which can hold anything together. Electrical tape is handy too.
Drill Either cordless or electrical will do. You will also need a variety of bits.
Level Even a small, inexpensive level can help your work come out straight.
C-Clamps These will hold lots of things you are trying to put back together.
Pliers A good, basic pair of slip-joint pliers can tighten, loosen and hold all sorts of things for you.
Wrench An adjustable wrench or a "Crescent" wrench can give you lots of extra muscle to tighten and loosen a variety of nuts and bolts.
Ruler A retracting flexible tape rule is compact, accurate and very useful.
Utility Knife Get one with replaceable blades.
Glue Household cement will tackle most things.
Fastners Buy a couple of inexpensive variety packs and you'll probably have what you need.
Sandpaper A basic variety pack should have what you will need for the average project.
Lubricant WD-40 is amazing stuff.
Flashlight A small, rechargeable flashlight is important for all sorts of emergencies.
Tool Box A lightweight, plastic model will hold most of this stuff plus a few of your own favorites. There are some nifty models that have some great features like a place to sit down!
Plunger A plumber's friend can also be your friend, especially if your toilet is overflowing!

There are lots of other tools we think you should eventually get but these are the basics.