Wow, I can't believe I didn't see this thread before now. Guess I've been spending too much time animating. :p I'll try not to repeat too much of what was already said (all good advice).
First off, about me. I'm a freelance animator in the game industry. I've been working on games for the past 6 years and have 9 shipped titles on my resume. I originally got hired at a game studio called Dynamix right after I graduated and worked there as an animator for 3 years until it was closed by its parent company Sierra. For the past 3 years, I have been doing all freelance work.
Doing freelance work is a mixed blessing. On one hand, you have the freedom to (mostly) pick and choose what you want to work on, and you set your own work hours. Working from home is nice as well, since I get to actually make full use of all the stuff I spent money on.
However, freelance work also means constantly being on the lookout for new contracts, managing business-related matters, handling clients, and, most important of all, forcing yourself to stay on track on your own without a boss looking over your shoulder. Freelance work is not for everyone. It takes discipline, motivation, and perseverence to survive as a freelance artist. I've been fortunate thus far, but it can be touch and go sometimes.
No matter what field or job type you get into, your portfolio and/or demo reel are the most important things in terms of getting you the interview. People often forget this. Your demo reel is not meant to get you the job. It gets the prospective employer's attention and gets you in the door for an interview. The interview is where they decide whether or not they like you and whether or not you are a good fit for the company.
Realistically, anyone can do the work. There are thousands of people out there doing what we do. What it boils down to is who you are as a person. If you have a great portfolio/reel, but you're an ass, no one is going to hire you. They don't care how good you are. If you're going to be a pain to work with, they won't want anything to do with you.
Bottom line is, as has already been said many times in this thread, stick with it, work hard, and constantly try to improve on your skills. It takes hard work and perseverence to survive in these industries. Don't give up. Sometimes it takes time to get the first job. Once you're in, it's a tad bit easier.
OK. Dissertation is done for now. :p