Having encountered a few former students recently, I was reminded of something that I think every student should know:
This is a hard industry to find your first job. There's a reason it's called "breaking in."
This usually hits home about 3 to 6 months after graduation. The student (well, no longer a student) applies to a bunch of game companies, only to either get rejections or dead silence. And then comes the self-doubt: am I not finding a job because there's something wrong with me? Am I not as qualified as I thought I was? If I'll make such a great game developer, why won't anyone hire me? Maybe I should've listened to Uncle Roy and gone into insurance.
Making it through that period is important. Once you're through, there comes a redoubling of effort: I just have to try harder. I'll apply to more places, and start looking for new opportunities that I might have missed. I'll call back those places I haven't heard from, just to check on things. I'll go back to the websites of the companies I was interested in and see if any new positions opened up since a few months ago.
And then on some idle Thursday, you get that call. And maybe it's your dream position that you thought was lost, and maybe it's QA at some local no-name casual games company, but at that point you've got what you were after: your first industry job.
Granted, it doesn't happen like this for everyone. Some students are lucky enough to line up employment before they even graduate. But I've seen the scenario above more often than not (and not just with my students, either), and it's worth a reminder that this is not a poor reflection on the student... it's part of the process.
If you're a student about to graduate (or recently graduated): bookmark this post, and return to it when you're looking for that first job and everything seems so elusive. Remind yourself that it's not you, it's the industry. So buckle down and try harder, and keep trying until you get a job.
If you're a student who won't graduate for awhile: remember that this can happen, and plan accordingly. Make sure you've got some way to support yourself for awhile after you graduate, if you have trouble finding a job making games. Take care of food/water/shelter first, and realize that finding game-related work can sometimes take awhile.
If you're a teacher: remind your students of this every now and then. It's easy to forget, but it's important to remember.