How do I share and play music in my office?

Check out 'play' from one of the guys at GitHub. Ive had an interest in it, but never had a chance to use it yet.

iTunes has this feature built in. Turn on iTunes DJ and let it play. Individuals using the Remote app (iTunes App Store link) can vote for the next song, or outright start the next song.

It's not a universal app, but being an iPhone/iPod app means at least it can run on iPads as well.

I haven't tried it (was interested by your question so I googled around) but Subsonic looks like a winner imho. Free download available for Windows, Mac, Linux and Unix.

Subsonic is a free, web-based media streamer, providing ubiquitous access to your music. Use it to share your music with friends, or to listen to your own music while at work. You can stream to multiple players simultaneously, for instance to one player in your kitchen and another in your living room.

From the features page :

Upload and download files to/from Subsonic, with automatic zipping and unzipping.