Another option is to use a CNC router but depending on your project, that may not be possible. Here's one method that I've used that works well and doesn't take much time.
I made this at TechShop Detroit.
Step 1: Laser Cut Your Guide
Make sure you don't have any narrow places that will need to be cut (or else the router won't be able to get in there) and try to avoid too many sharp turns. The smoother a shape is, the better it will be.
When you're ready, use a laser printer to cut out the shapes onto a piece of masonite or hard board. I was able to find a piece large enough in the scrap bin next to the lasers at TechShop. It measured approximately 4"x24".
These are the settings I used for an Epilog 60w laser:
It cut cleanly through the material without leaving any noticeable burn on the material.
Step 2: Prepare Your Router
The trick here is to use a router bushing that allows your router to follow an edge. I got mine from Rockler. Harbor Freight also has a 7 pack available for $15.
Install the router bushing into the bottom of the plunge attachment for your router. It just screws in and clamps itself between the base.
Again, make sure your router is unplugged. Insert your desired router bit. I used a 1/2" straight cut bit. A smaller bit will give you smaller inside radius corners.
Before continuing, grab some safety gear. Routers generate a LOT of noise and dust. Wear safety glasses, ear protection, and a respirator. Wood dust can be nasty and you don't want to breathe it in.
Step 3: Prepare to Cut
Set the depth of cut on your plunge router. Using the built-in stop, you can set the desired depth before you start. This way, when you plunge into your material, you won't go too far.
Additionally, with your plunge router, you can use the rotating step to go incrementally deeper with each pass. This is a good idea if you plan on removing a lot of material. Don't do it all in one pass. Take off a small layer. Turn off the router and step down to a deeper cut. Repeat until done.
When you're ready to cut the material, insert your router into the jig so that the bushing is sitting on the inside edge of your pattern. With the router off, just make a test pass making sure you'll be able to trace the entire pattern. Check that nothing will get in your way (no tripping hazards for you and no clamps or tools in your trace path).
When you're satisfied, make your first pass by starting the router and plunging into the material. Trace the pattern by placing light pressure against the router so the bushing rides right along the edge. If there is still material on the inside of your shape, make multiple passes to slowly remove it. Repeat until you've reached the desired depth of your cut.