Table Saw
Getting started at woodworking can be a very intimidating thing.  In addition to trying to learn a new set of skills, there is the issue of trying to figure out which tools you will need.  If you look at a catalog or web site for a company that specializes in woodworking, you will be flooded with images of power tools and hand tools.  It can be a very daunting task to figure out which ones you should start with so that you can get started on your journey to learn how to woodwork.
Below is a list of the 5 tools you should get to start woodworking.  There will be other tools that you will want down the line, but these are the important ones that will get you started and allow you to build a number of projects.  With them you will be able to develop your skills and produce some really cool things that you can be proud of.
1. Table Saw
A table saw is a foundational piece of the workshop.  With it you can rip boards down to the right width, cross-cut boards to the right length, cut a bevel along the length of a board, and make miter cuts as well.  If you throw in a dado set, you will be able to use the table saw for cutting grooves and tenons for mortise and tenon joints.
There are also many sleds or jigs that you can build to make it even more functional in the shop.  A simple cross-cut sled will make it even more effective at safely making cross-cuts.
2. Compound Miter Saw
The compound miter saw is really valuable for being able to cut boards down to the right length, and for any angled or mitered cuts that you need to make.  Some of the functions you can achieve on a table saw, but they are much easier and safer to do using a compound miter saw. 
Another key reason a compound miter saw is included on this list is that it will allow you to operate in a much more efficient manner while making precise cuts.  If you have a number of boards that you need to cut to the same length, you can quickly do it on a miter saw using a stop on one end at the desired length.
3. Router
A router can do a number of things for you in the shop.  The most obvious place where you will use it is in applying a decorative edge on a piece.  A simple round-over bit or chamfer bit will allow you to put a simple edge on a table top that will make it look a lot better.  
If you opt for a plunge router, you can add a spiral-cutting bit to make mortises for a mortise and tenon joint.  A mortise can be cut in many different ways, but doing so with a plunge router is pretty easy to do and will allow you to bang out a number of mortises in short order.  
4. Jigsaw
A jigsaw is a very valuable tool for cutting curves.  As you progress in your skills, you will probably end up upgrading to a bandsaw, but a jigsaw will allow you to do a lot while being less expensive, easier to store, and easier to operate.
Another scenario where you can use a jigsaw is when breaking down long boards.  If you buy longer boards, they can be quite cumbersome and tough to get up on a compound miter saw or a table saw to break down.  Taking the jigsaw down to the board is a much easier proposition.    Put your board on some supports on the ground, and then use the jigsaw to break it down to the lengths that you need for your project.  
5. Jack Plane
So far, we have focused on power tools, but hand tools can be equally important (and some would say, more enjoyable) in the workshop.  My recommendation is to start with a jack plane.  It is a good multi-purpose hand plane, and is a good starting point for getting used to working with hand planes.  
A jack plane is great for jointing edges.  Making sure that the edges of your boards are as square as possible will make assembly of a panel much easier.  After assembling the panel, you can also use the jack plane to level out any high spots to get to a smooth, level surface.