There is such an app. It’s called FileBrowser and it works on iPhones and iPads. An iPad recently came into our home – we bought a used one from a friend. I had the same question as you, so I Googled around and found that FileBrowser was highly regarded, I found their website, (the manual is there to read) and asked some questions and got nice replies.
Anyway, we put it on both the iPad and iPhone and it works well. It connects to any device on the home network , like PCs and WDTV. Here is how we set it up: There are hard drives connected to our WDTV, one has over 9000 tracks in the iTunes folder on one drive, and there are videos on another. We can stream any of the music from the drive through the iPad and iPhone. As for videos, there isn’t enough “guts” in either i-Gadget for too complex of a video file, but it plays mp4 files just fine. The manual says to use another program called CineXplayer on the iDevices to play avi files. Unlike streaming music files and mp4 video, the CeneXplayer has to download an avi file to the iDevice and then it can play it. In my experiments, the avi video is not smooth, as it hesitates ever so slightly periodically every few seconds as it reads more data. This may be a function of our iPad being the original model. iPad2 has more guts, so may do better.
Anyway, this is the home website for FileBrowser: http://www.stratospherix.com/