Unsurprisingly, you can purchase many or few items, and, depending on how ambitious you are, how deft you are with your hands, and how patient you are, you might find that you can get by with very few items -- or that you need a lot, and make use of each one.
For example, if you want to cut the fat into flour when you make a pie crust, you can do it with two table knives from your silverware drawer (cost: $0), used in opposition to each other (think of cutting in different directions); or a pastry blender, which has 5 or 6 curved wires attached to a handle and makes short work of the process (cost: $7-$10); or you can use a food processor (cost: $200 and up, depending on size). Of course, you already have the table knives, and they get used for other things (we hope!) and the food processor may already be in your kitchen, and it is also handy for other things. But if you are a beginning baker, and want to get a few good items for your batterie de cuisine, we'd recommend the pastry blender -- it is more efficient than the knives, cheaper than the processor, and will give you more of a feel for the dough and the process than the processor would.
The processor has become essential for other things, at least in our kitchen. It is indispensable for chopping nuts, making crumbs out of graham crackers, grating carrots for carrot cake, and grinding chocolate into a powder for babka. A blender doesn't do any of these things well, since solids fall to the bottom and clog the blades. Of course, you could chop the nuts by hand, smash the graham crackers in a plastic bag with a rolling pin, grate the carrots (and your knuckles, no doubt) by hand, and -- well, maybe grate the chocolate, or chop it. But you'd have a mess (the chocolate held in your hand will melt, and about a third of it will fly all over the counter), and the food processor will do each of these tasks in mere seconds.
A recent development (at least, since we were young) has been heat-proof (usually silicone) spatulas. These come in a lot of fun colors (which is useful if you want to remember which one you are using for what) and can stand high heat, typically up to 450˚ or 500˚F. When you are melting butter, chocolate, or cooking anything on the stove, you can stir and scrape the pot with one of these, and you'll possibly prevent your mixture from burning. (For omelette lovers: I don't know how anyone ever managed to make an omelette without a silicone spatula and a non-stick pan. The combination is unbeatable.)
I've already written in a previous post about the usefulness of both digital scales and instant-read thermometers; you can go back and read what I have to say about them. I consider both of them essential to accurate baking.
My mom had one set of measuring spoons and one set of measuring cups (clear Pyrex ones, intended for liquids). Somehow, she managed to be a top-notch cook, but I'm not sure how! I've lost count of how many measuring spoons I have; it seems a great luxury to be able to snatch up a clean spoon to measure, say, baking powder, when I've already used one of the same size to measure vanilla. Instead of having to wash and dry the spoon in between, I just keep working. And measuring dry ingredients in a liquid measuring cup (assuming you're trying to work with volume instead of weight) is a headache; using the dip-sweep-pour method is so much faster and more accurate. And do beware of clever, cunning, beautiful, yet inaccurate measuring spoons and cups; there seem to be many out there in gift shops, and I wouldn't tell you not to buy them, but they are often best used for decoration, not measuring. Check them against utilitarian utensils of known accuracy (or proven utility). I would think that two sets of measuring spoons, one for wet ingredients and one for dry, would be a minimum. Get different sets, so you can tell them apart at a glance; if you are buying plastic, get two different colors, or get one set of plastic and one of metal. And please get a set of dry measuring cups (these are the ones that look like little saucepans) that measure up to the very top; a few indicate that to measure one cup, or one-half cup, one fills to within a fraction of an inch of the top lip. These are worse than useless; you will end up with failed cakes and cookies, if you use them, or will end up throwing them away in frustration. Any of the major brands of oven-safe glass is fine for liquid measuring cups; Pyrex, Anchor-Hocking, and Fire King are some of the best-known ones. They can go in the microwave and the oven (but not on the stove-top) so you can melt butter or heat liquids in them. In the past decade or so, Pyrex has started making cups with handles that are hooks instead of loops, so the cups nest, and some have a lot of head-room at the top (above the measuring markings) so that you can, say, measure a half-cup of milk and a quarter-cup of oil, and then beat into those a couple of eggs. Now you've mixed up all the wet ingredients needed for scones, pancakes, or other quick breads, and only dirtied one cup. Aren't you smart?