I am new to Macs and in my office there are a number of Mac users, and a few of us PC users. The Mac users all have either OS X version 10.3 or 10.4. I found some software which I would like them to use for an upcoming project, but it is only available on Linux. My question is this; is it possible and how easy would it be to run linux software on Mac OS X? Obviously I don't want to force them to boot into a linux box in order to do their work, so I need to know if I am looking for a linux emulator or if this capability already exists, or if this capability doesn't exist. Thanks.

As i understand it, it would matter more whether it was compiled for the mac or PC processors..(PPC vs. Intel)..
As Mac OSX and Linux are both unix variants, and share something called 'posix' compliancy ( a unix standard), then theoretically there should be a lot of cross-compatibility- however, linux apps compiled for the pc are just as incompatible with macs running linux as they would be on OSX.
I'm not an expert on this,however, so any more replies would be welcome..

This totally depends on the software in question. There are Linux apps which run in OSX. The more complicated the application, the less chance you have of a simple compile-and-run. A GUI will require X11, which can be installed on OSX (X11.app). Fink will help you here.

If modifying the client is a too tricky, consider running X11 apps over the network. You can run the terminal client under Aqua. Apple has a distribution of X11, as I mentioned.

If you do end up needing to port apps over a network a cheap solution is nomachine

It has been benchmarked right up there with a citrix and tarentalla server but is only a couply hundred for the official release (there is an open source port for free)

Just like citrix it can or a basix x display it can export singly apps or entire desktop..