Can I have my itunes library on more than one computer

Question

I want to add to my library from a couple of different computers and not have to use the same one all the time. Can I have Itunes on 3 different computers and synch the libraries?

Answer 1

It is possible but requires very careful organization.  Essentially you need to replicate your library from one PC that you designate as the "master" to the others you want to use the same library on.  See these two of turingtest2's user tips:
Make a split library portable describes how to bring your library into the best layout to make it easy to replicate
Backup your iTunes for Windows library with SyncToy describes a robust procedure to copy your library to an external drive, and then to make incremental updates to the backup
This is essentially the approach I use, with three different PCs - desktop running Win7/32 as "master", two different Win7/64 laptops as "secondary":
You'll notice that everything here is one-way, from the master, via the replicated library on the external drive, to each of the secondary systems.  It is possible to reverse the process under very specific conditions - an example's best here ...
I update the backup on my external HDD from my master system
I update the library on one of the "secondary" laptops from the external HDD (so this is now a 100% duplicate of what's on the master)
I add to the library on the secondary laptop - new media, modified playlists, etc.
Now, assuming I've made no changes to the master since step 1, I can reverse the process - backing up the library on the laptop to the external drive, then updating the master from the external drive.
The last time I posted this picture/procedure it was suggested that I should accompany this with a "health warning", so here goes - YOU REALLY NEED TO KNOW WHAT YOU'RE DOING for this to work correctly (or, like they say on TV, "don't try this at home") - there are many ways for this to go wrong and really only one way to ensure it works correctly.  The whole approach is predicated on the assumption that you have two (or more) libraries with identical content.  Even then, I tend to steer away from the situations where I modify the library on one of the secondary systems and sync this back to the master - not because it doesn't work, but because it opens up a few more possibilities for "dumb user error" that could leave me with inconsistent content across the three machines.
The other possible solution, which would be an option if all the machines you're using are on the same local network, is to use Home Sharing and make use of its facilities to copy media from one library to another - in this case you have distinct libraries with a method for copying content from one to another.  You won't, however, be able to have the same playlists on each machine.  The other benefit of the approach described above is that because you have several physical copies of the same logical library you can sync your iDevices to any of them without the possibility of the device content being erased because iTunes detects that its previously been synced to a different library.
I'll be honest and state that it took me considerable time to arrive at this setup - with more than a few ****-ups along the way - so you may want to carefully test this out before implementing something like this across several systems.