I want a program like the Remote app for the iPhone, that will run natively on Windows, OSX and Linux. Any suggestions?
It's not fancy, but using VNC or a remote desktop app of some kind would work.
There is iTunesRemote, in the downloads section it looks like they have apps for OS X, Windows, and Linux. The version numbers are pretty low though.
If you have a supported phone and bluetooth you can probably use Salling Clicker on OS X and Windows.
Here's a hardware solution for Windows and OS X.
There doesn't seem to be much in the way of Windows or Linux apps to do this however. iTunesRemote looks to be the best option I can find.
Tunes Remote SE is the way to go!
It's just perfect, cross-platform (developped in Java), with an UI similar to iTunes, let's you see the whole library and covers (not just "play/next/pause"), and even Genius mixes!
After looking at the accepted answer options and not finding anything I liked, I came across TuneConnect (version 2 was out at the time of writing).
Free, open source and it does exactly what I wanted to do. The only downside is it's OS X-only, but at least it's a good looking OS X app that fits nicely in to the OS X workflow.
If you are just wanting to play itunes shared libraries, you can just use itunes on a computer and connect to a shared library. I know it is not a small remote like app, but it works.
Unless you mean control what is playing on the computer containing the itunes library from another computer? That I do not know what solutions are available.