1. A scroll saw.
Obvious, yes, but you want to make sure you get the right kind. A 16" usually works best for a wide range of projects, not just scroll saw artistry.
2. Drill Press.
You will probably only need a small one, one that you can place on top of a work bench. You will also want many different sizes of drill bits, and lots of small ones, because those small drill bits can break pretty easily.
3. Printer.
You probably don't want your printer in your shop necessarily, but you do want a good quality printer to print out your patterns with. No need to spend too much money on one though.
4. Adhesives.
I know a lot of people will use tape to secure their patterns onto the wood to cut out. I don't like doing that, because the blade can snag the paper, and then it is hard to tell where to cut. I prefer to use rubber cement, because it secures the paper down nicely,and it's easy to peel the paper off. Then all you have to do is get some sand paper to remove the remnants of the rubber cement. Spray-on adhesives work well too.
5. Blades
You will want a wide variety of blades as well, varying in terms of tooth size, some with reverse teeth, thickness, and tooth distance. Personally, I hate to use spiral blades. Yes, it's easier in terms of making turns, and cutting in any direction. But the cuts are not usually very smooth, and spiral blades tend to snag the wood, and yank your project up. Ever since I used a spiral blade, and it snagged the wood, and broke a vital piece off of it, I have been staying far away from spiral blades.
6. Stool or chair.
Scrolling, especially scrolling with a lot of tiny detailed cuts, is a long and delicate process. You probably aren't going to want to stand the whole time.
Ok, that's just a basic rundown of what you will need. I honestly can't think of what else you would possibly need.