There is a wealth of tools available in stores and online, even if you could simply buy them all, you'd need a warehouse just to store them. That being the case here's a shortened list of; the essential power tools every woodworker needs in a well equipped shop.
Saws are the backbone of a well equipped shop. And there are many different saws to choose from, essentials for any woodshop, are at least one of these three most common saws: a table saw, a compound miter saw, and a radial arm saw, depending on your needs.
Table saws are a fixed blade, on a fixed table. You can adjust the blade height, and the angle up to 45. To cut with this saw you make the proper adjustments and guide the wood into the blade with the help of a fence, push stick, and sometimes a miter gauge. You can make almost any cut you need with this saw, and it is essential if you're cutting large sheets of plywood.
Next is a compound miter saw, sometimes called a chop saw by old timers, because, that's an exact description of how it works. You place the stock against the fence, grab the handle, and with the blade spinning, chop the wood into two pieces, a limitation with this saw is you can't cut dado joints, or other common cabinet joints, but it's the saw you needs for outdoor construction. It's great when you are cross cutting stock with dimensions as large as 4x6, typically used in heavy duty deck construction, and garden border projects.
A radial arm saw combines the precise cuts of a miter saw, and the versatility of a table saw. You can on an angle cut stock; you can tilt the blade to cut the face of stock, you can cross cut wider stock than a miter saw, because the radial arm is also a guide that the saw rides on when you pull the saw through the stock. You can also adjust the cutting depth to make fine cabinet joints, and finally you can lock the set the saw to rip boards up to 12 wide. A notable limitation is you can only make relatively narrow cuts on plywood, where a table saw doesn't have this limitation.
If you are mainly construction oriented, you'll need a circular saw to go where a compound miter can't go, and a reciprocal saw for tears down existing structures with ease. A laser level is a relatively new tool that that replaces a transit, level and plumb bob in one fell swoop. It is for use outdoor and indoor use, wherever a level line is needed, laying out a plumb and level deck, and indoors when you're installing cabinets, or even hanging picture frames true and level.
If you're mainly working as cabinetmaker, you'll want the square edges on your boards for gluing, with a jointer, and a planer. There are combination units available that square the edge of the board with one blade on the jointer end of the machine, and plane the surface of the board with the planning blade in the body of the machine. With this machine your stock will be trued up square, and a trimmed to identical dimensions essential for professional looking glued panels.
After your boards are trued to the proper dimensions, consider a plate joiner and biscuits, to lock your boards precisely in place for gluing.
A router is invaluable for cutting precision joints in mating panels. With the help of a jig you can make dovetail joints, which are the strongest and longest lasting joint in cabinetry. A router also dresses up the edges of your project with convex, or concave curves along the length, or more decorative edges.
Jig saws, and band saws allow you to cut patterns no table saw can do. There are hand held jig saws, and jig saw tables. These saws can cut any pattern on the perimeter of your stock, or inside the wood panel, with an access hole, predrilled inside the middle of your pattern, but are limited to stock less than a few inches thick. A band saw can handle larger stock but can't cut the interior of the panel, unless you slice your way into the pattern, and that slice doesn't affect the integrity of your project.
You may want a belt sander if you're working on large projects, or an orbital sander for finishing work. There are also sanding tables, which have belts fixed on a flat table face, and sometimes they have a sanding wheel with adjustable bevel table for intricate work. In the same family are grinders, which are not for working with the wood itself, but for dressing the tools a woodworker often needs to use. Once you own a grinder, you'll wonder how you've ever worked without one.
Drills are another essential tool in your tool chest. You'll need at least one electric hand held drill, and you'll really appreciate a cordless model that can go almost anywhere. Cordless drills also switch easily from drill, to heavy duty screw gun, with a quick change of the tip. For more repetitive drilling you might want a drill press that can be set up to repeat identical holes, locking in exact angles and precise drilling depths.
Finally dust collection, don't over look this important workshop task. Many power tools have ports for the attachment of a shop vac. When sawing and sanding the dust accumulates quickly. Collecting the dust while it is being generated will save much time over allowing the dust to settle on every other piece of equipment in the shop. It's less work to move the vacuum to the machine and attach the hose, than to chase all the dust where ever it may land. If you have a helper, and run multiply machines at the same time, consider a dust collection unit that can handle multiple machines running at the same time.