I've had some luck with Brad Bolthouse's LithUnwrap freeware utility. It's like Steve Cox's UVMapper, but supports multiple file formats, has a hardware-accelerated 3D texture-shaded preview mode, etc. Anyway, I tried it this afternoon, successfully loaded one of my .md3 models, and then saved it to .obj format. I won't guarantee that it'll work with every .md3 model, but it can do the job.

Download LithUnwrap at one of these locations. If one site is down, try the other; it's a popular tool for game modellers, and Bolthouse is constantly updating the code, so the sites get visited often, and the hosts have to shut them down occasionally.
Mirror site #1
Mirror site #2