Yes, it's possible thanks to this neat little utility I found. It's called RSS Streaming Tools. It works by exploiting the PSP's built in RSS 2.0 capabilities. All that's required it any desktop or laptop PC running Windows and a wireless network router. Right now, the program allows you to access only MP3 music files on your computer but there are plans that would allow for video streaming as well. Also packaged is the ability to stream online radio stations through ShoutCast and Youtube video. The program is currently in it's Alpha stage, meaning that it's still under construction. However, it does an excellent job of streaming MP3 audio and it's easy to use.

This is ideal for PSP owners with large music collections that exceed the capacity of their memory cards. The program is 100% freeware and its virus free. Check it out.
PSP Streaming Tools

I also found a guide that allows you to set up your own streaming network for the PSP. It's complicated but it allows you to stream to PSP if you own a Mac OS X or Linux computer. I believe this should also allow you to stream video content as well. I couldn't get it working properly on my Windows PC but you may have better luck.
Streaming Music From Your PC to your PSP