Good news! There's now a way to run UMD-only games on a PSP Go. The bad news: it's an unofficial exploit. Coders "Virtuous Flame" and "Coldbird" have released a "Homebrew Enabler" for PSP firmware 6.31 and 6.35. Using that, "Liquidzigong" was able to get the Prometheus ISO Loader program running on the disc-free handheld, allowing copied UMD disc images to be saved and run on the system.
After the break, you can see a demonstration of the hack, in which a user loads up Kingdom Hearts: Birth by Sleep -- a high-profile title never released on PSN. While we can't speak on the legality of using this method to back up your UMD games and play them on a Go (and then on the go), we can confidently condemn the use of this exploit to play games that aren't yours.