I'll go right to the point. I'm writing this on my friend's behalf. He's a computer science major (senior) and currently an intern at the IT support somewhere. He was asked to come up with a project idea that benefits his department and bring it into reality. It definitely has to involve programming. His department uses BMC Remedy, and they prefer something that has to deal with it.
So, ideas please? Thank you! :)

Well, seeing as how you did not provide what the company does, we can not really give you a specific application to code. I know when I was a senior is high school(last year), I created a chat program that allowed you to chat with people across your network. I created this to talk to friends in class :D, but this could really be useful in all companies as they could use "their" own chat software to communicate to one another easier. Below is an image of my application so you can kinda see how I planned it out.

My Chat Program:

If you would like, kinda give me an idea of what the company needs and does and I will try to spout out some more ideas. Also, the best way to get an idea for an application, in my opinion, is to find out something that you need done and make an easier to do in your own way.

It is a diversified manufacturing company, active in chemicals and intermediates, industrial polymers, fertilizers and metals. His department is all about IT support, as I have mentioned.

I suggest you write a small ticket/fault reporting system.

That has a lot of the key things most Universities will want to look for.
Classes, Inheritence, Databases, Network Communications, UI Design etc. :)

(You could also expand this into Web Development as well)