Laser cutting is a good option, if you have access to a vector-graphics program (like AutoCAD or Illustrator) and the piece isn't too small. Really narrow pieces tend to melt in a laser cutter.
Band and scroll saws also work, but as Warptiger mentions, some saws have trouble handling thermoplastic (meltable) plastics. You can try adjusting the speed of your saw (on my saw, slower speeds equal less melting). Using a narrower blade or a blade with fewer teeth may also help.
My band saw tends to leave a rough edge. If yours does too, you may need to cut your pieces a little large and then sand them to the correct shape. Files, sanding blocks, belt sanders and Dremels (especially Dremels with "router tables") are very useful here.