If you are on a Mac, try control-clicking on your file and tell it to "Open with" and select iTunes. If you don't see it on the list, select "Other..." and look for iTunes.

Make sure that the type of file you're downloading is an .mp3 and not a .wmf, as iTunes doesn't seem to recognize them as sound files.

You might also want to consider LimeWire Pro, if you don't already have it. It creates a LimeWire playlist in iTunes and copies all downloaded music to that playlist so you can easily find and play it.

Hope this helps!