I attended a talk by Chris Klug [MobyGames rap-sheet], former creative director of Electronic Arts' MMORPG, Earth & Beyond, at Carnegie Mellon's Entertainment Technology Center. Klug came to the videogame industry by way of the pencil & paper RPG industry [Exhibit 1, Exhibit 2], and spent much of his early working years as a professional theatrical lighting designer. As somebody who changed from one field to another perceived (mistakenly, he believes) as being very different, he had quite a bit to say on how you, too, can get into not just the games industry, but any industry.
A word of warning: Klug's answer to the question "How do I get a job?" is, I'd say, roughly the equivalent to answering the question "How do I get in shape?" by saying "Good diet and regular exercise." Those of you looking for silver bullets had best stop reading and look elsewhere. Also, this is, of course, largely opinion, and I didn't agree with everything he said, so no guarantees.
The first thing to do is figure out why you are unique. This is not easy, but there you go. This is important because it is a part of answering the question, "What do I really want to do?" not simply in the sense of job title, but in the sense of discovering your unique vision, which you bring to everything you do. This is the sort of thing that you need to show an employer: what you bring to them that they can't get from anybody else. Companies hire people, not skills, so when you're out there trying to sell yourself, make sure you're really selling yourself.
From here on out, it is all about who knows you. The amount of time your favorite game company is hiring for a position ends when you finish this sentence. By the time you know about it, it's too late, so you have to make them know you. That way when they get the word that money has been allocated to hire 3 new Postion-Xes, your name immediately spring to mind.
Think of a person in the industry whom you admire. Think hard. Research this person. Take your time doing this. If they're giving a talk at a conference, attend the talk. If they've written papers, read the papers. Wrap your mind around this person's work. Take your time doing this. If you still admire them at this point, you're doing okay. If not, start over again with somebody else you admire.
Now, contact them. Somehow. If they can't be contacted directly, go through their office. Show that you admire them, but also that you know who they are (that's where the research comes in). Tell them that you'd like to enter the industry, but what you really need is some advice. Try to get the names of 3 other people that you can talk to. Contact those people, explaining how you got their contact information, ask for more advice, and see if you can get 3 more names from each of them. Just keep doing this. This is how you make people know you when you haven't done anything yet.
And never, ever ask for a job. They will say no, and you don't want to ever put these people into a position where they have to say no to you. Just keep asking for advice and for more people to talk to.
Once you've made contact with somebody, every few months or so, send them an "update" email, talking about what you've been up to recently. Write it like they would care. Worst case, they delete it right away. Best case, they read the whole thing. This is how you make people remember you.
Basically, you're letting the universe know that you're available, one person at a time.
Don't trust making Neverwinter Nights mods or Unreal mods or levels to sell you. Don't trust your awesome website to sell you. Hiring decisions get made at bizarre times and bizarre places, and your demo is meaningless if they aren't at their computer, or don't have the game they need to run it. Still, if you have these things, don't neglect them. Every single thing that you use to sell yourself, from resume to website to demo reel, must be able to sell you 100%, because there is always the chance that it's the only thing they'll ever see.
This isn't a quick fix method. You could follow Klug's advice for years without getting picked up anywhere. Nevertheless, if you have the skill, the passion, and the endurance that would make you succeed in the games industry, Klug's a good man to listen to.