First I'm going to start out with a career of actually playing video games. The first thing that might come to mind is reviewer. If you're interested I'd recommend getting involved with a local paper right away. Most likely this will be a school paper, and will most likely be done on a volunteer bases. This will give you a good start in journalism, and you may want to look into getting a BA in Journalism or at least take a couple classes at the college level. This will help you get the needed base to start as not only a game reviewer but a game journalist who can cover major press releases, and other game events. It also surprises me how little journalists actually know about journalism law so getting a quick background in that can give you a great edge if you manage to get an interview. One thing a lot of people probably don't realize about this job is you tend to work a lot more hours than normal and it really ends up being two jobs, one for writing about games, and another playing them. You also have to play a lot of really crappy games and unlike normal gamers if you don't like the game you still have to thoroughly play it.
The other guys who get to play games all day are the testers. Testing doesn't really require to many skills just a strong will to do repetitive actions, and having good enough communication skills to describe what you come across. "I was doing that thing, and then the game started bugging out" is not good communication. With testing the hours suck, the pay is low, and odds are you'll hate the game you're testing. Honestly I have no clue why some people think this is a good job, but it is an "in" to the gaming industry and can get you connections which I'll talk about later.
The last person I'll talk about is the professional gamer, and though a few pro gamers can make a ton of money at tournaments, and through sponsorships lots of other pro gamers make their money through teaching. If you have excellent knowledge of a game and can easily get clients you can get paid pretty decent teaching others the stuff you had to learn the hard way. The hard part about this job is getting those first initial clients who (if you are any good) will pass your name to others looking to gain some "skill" without putting forth hours and hours into a game. Few people have the skills to pull this job off, but it's still worth mentioning.
Now I'll get to the game creation careers which I'm sure most of you are mostly interested in. First when starting your career in game creation you need to figure out which category you fit into which can mostly be broken into programming, or artist. Lost of people currently in the in the industry are hybrids, but once doesn't have to be since most developers are looking for specialized professionals. For these jobs you will need a few things. First people in the gaming industry need to actually know who you are. Few game jobs are publicly advertised and many game HR departments get tons of resumes/portfolios every day so trying to get a job based on that is pretty much like playing the lotto. You really need to do alot of social networking and talk to people in the same field. Communication is huge in game development, and is an essential part of getting a job. Next expect to move to an area where game studios are located, very few jobs in this industry can be done remotely.
Most people think that programming is the only way to get into game creation, but honestly there's a lot of people in the industry that don't do ay programming. Still it's fairly common so I'll go over it. Like the job says to be a programmer you have to know how to program. There's tons of different programming languages to learn and the more you can learn the better chance you have of getting a job. Most people find a CS degree pretty helpful, but a portfolio can show off just about the same amount of knowledge. To start off I suggest learning any programming language (C#, C, C++, flash, heck even scripting is a good place to start). Good news about game programming is the pay is very high. The bad news there's tons, upon tons of programmers out there to compete against. Still if you start programming and you love it (some people actually do) you'll eventually get really good at it. If you don't like programming it's not something you can really force, you may learn a few skills, but you'll never be any good if you don't love it.
Next is the art department which is pretty diverse in games. I'll start from beginning to end sort of. First you have the concept artist who in the early part of the games development creates the art which will become the reference for the entire game. This is often done with traditional art tools (like paint, and brushes). For this job you need to be a really well established artist who can work quite fast, and one of the few jobs you can actually work off-site. Other artist jobs are the texture artist, and modeler. Technically there are a lot of other jobs but it breaks down to these two skills. Texture artists tend to progress a bit more with traditional art skills along with some insane Photoshop skills. They've got a great eye for detail. The modelers tend to be more technically attuned being skilled at 3dsMax, and/or Maya many know these complex programs in and out. More and more artist jobs are requiring a traditional hand art skill which tends to keep a lot of people away since they figure it's a natural talent, but I've seen quite a few people learn these skills over a matter of months quicker than they learn 3d programs, or Photoshop.
Now learning the skills needed for game creation doesn't come easy, but a great thing about the game industry is that many developers are not too picky on a college education. Therefore you can save thousands teaching your self, provided you know what you need learn, and have the mentality to actually do it on your own. I would say schools tend to have a much higher success rate, and better guidance towards what to learn and where to learn it, but if your not serious you'll fail either way.
There are a few jobs outside the visual arts and programming I should probably mention. Audio plays a key role and can be an avenue into the game industry for audiophiles, or even a few voice actors. Also public relations, and game business are growing industries that need experienced people that understand not only understand games, but those that also understand how to run a media campaign. Far too often good games are ignored because publishers/developers didn't hire the right people for PR. Also storyboarding, and writing for games is becoming more open to outsiders, but I wouldn't count on it.