These are just the tools I have right now. I'm not promoting any specific brand.
First up, Portable drill. You can't say enough about a good, heavy duty portable drill, lots of drill bits and an extra battery.
Palm sander and/or sheet sander: One of the handiest and most useful electric tools to have. Buy some variety packs of sandpaper to go along. There are all sorts of practical uses for a palm sander, plus it's cute.
Jigsaw: Come on?! Can anyone do without a jigsaw? Cutting out circles, headboard designs or even Christmas Tree ornament shapes can't be done without a sturdy, powerful jigsaw. A good variety of blades is a must.
Dremel: I don't use my dremel much but mainly because I forget about it. It's hanging off of the side of my workbench and I overlook it when my palm sander is on the shelf. The dremel is versatile and can cut, sand, shape, drill, buff, polish, etch and more.
Router: I've purchased my first router upon the salesman's recommendation but I haven't gotten around to using it yet. I bought it to cut a groove 5 inches from the edge of a headboard frame so I could set in a piece of cording. A router can also do professional beveled edges, cut grooves, shape, drill and carve.
Upright Belt Sander/Bench Grinder: I bought this a while ago when I was making decorative knobs with polymer clay. It was a little hefty for my purposes, but I've used it for quick filing down of wood pieces and polishing wood furniture feet with the padded disk attachment.
Small Bench Grinder/Polisher: This is the smaller grinder/sander/polisher I got for the knobs. This is also a good polisher for all things small.
My New Favorite: My mini-air compressor (68.00 at Menards). This little tank is portable, powerful and noisy. I hook up my upholstery pneumatic stapler and cover chair seats lickity split. My big compressor is in the basement and it's too cumbersome to haul upstairs.
Upholstery Staple Gun: If you think you'll be recovering a fully upholstered chair and more through the next couple of years, this stapler is IT! It runs about $129. It's lightyears above the hardware store electric staple gun.
Electric Staple Gun: Available at all hardware stores. They'll tell you it's a gem, but beware! The staples seem to crumple up when shot into plywood. If you're doing something lightweight, these work satisfactorily. I just haven't had that much luck with an electric staple gun and I wouldn't even attempt the UNPLUGGED version. (No photo)
Heavy Duty Glue Gun: I don't even need to say anything about this necessity. Don't waste money on the itty bitty ones. Buy plenty of glue sticks for all temperature settings.
Heavy Duty Sewing Machine: An inexpensive Singer or Brother machine is great for lightweight frocks and such, but the real DIY Girl needs a heavy duty machine for shower curtains, couch cushions, dog beds and drapes. I have approximately 12 sewing machines and one ginormous Consew Upholstery Machine that can almost sew two slabs of concrete together. Get a machine with all metal parts. The plastic parts just wear out way too fast and the lightweight machines vibrate themselves all over the place. Ebay is where I've purchased some good old heavy duty machines.
And a more versatile workhorse:
Miter Saw: Crown molding, base molding, and quarter round will all require a miter saw. I use this for cutting multiple pieces of wood posts or 2 x 4's that need to be the same length because it has a nice little backboard piece to stabilize the wood. My husband has done all the molding work. I'm going to learn how to make picture frames this year and the miter saw is a must to cut the 45 degree angles.
Circular Saw: I only use this when I'm making a long straight cut. It's not a must for the casual DIY Girl, but it comes in handy and isn't that expensive.
My Wish List: Band Saw. The advanced version of the jigsaw. Oh, the things I could do if I only had a band saw.....
Other power tools and gadgets the DIY Girl may enjoy: soldering gun, woodburning set, Sawzall, small chainsaw (to make a side table from a tree trunk), small welding equipment, and all the accessories and materials you can find to keep her busy.
IMPORTANT: Follow all safety precautions and always, always, always wear GOGGLES!