(Speaking as CEO of a games company:)
I've done a lot of recruiting in the past, and made at least as many terrible mistakes as I have had great successes :(. I'm probably reasonably representative right now of many execs at other game companies who do hiring (although I'm no longer in the front line, so to speak ;) - although YMMV.
In addition to all the generally true things (several of which others have mentioned above, its all good stuff), with games-dev hires I'm really concentrating on the following:
1. Is this person lying through their teeth? (Happens often, sadly :(
2. If I sit this guy down at a desk and leave him, and give him a task, will he have the initiative to get it done, even if that means doing lots of background reading (spending ages searching google, AND reading it all), finding a well-respected book, ordering it off Amazon, designing a solution from his new-found-knowledge, and then coming to me to check if he's "going in the right direction".
I've had more than one person who would get no further than asking his colleagues how to do it, and if they didn't know, he might do a single, 2 minute google check, and then give up and wait until the next meeting before telling me (and so waste a week doing less important stuff).
3. Is this the kind of person, that when he accidentally breaks something (and spots it), will spend time fixing it, or at least TELL everyone else about it, and explain why he hasn't got time / can't fix it himself. (One guy used to keep quiet every time he broke things, because he didn't want people to think he was less than perfect. Wasted many many many man-weeks because we lost stuff due to the broken thing (which no-one had been warned about), then had to get lost work back again, then had to work out what the problem was, and finally volunteer someone to fix it!)
4. Is he a really fast learner? (no time for slow-learners in this industry, I'm afraid)
5. Script-kiddie or Super-Hacker? (Listing the languages you know usually screams "SCRIPT-KIDDIE!" loud and clear, at least in the games industry, because sadly many many wannabe games-developers who have very poor skills try to hide this fact by substituting quantity (of skills) for any detailed description that would show the lack of quality. For each language, give 5 words listing the kind of things (apps?) you have done with that language, that let me get a good idea of your level of experience with it!).
6. Innovator, or copy-cat? I've seen lots of C.V.s that e.g. mention "I wrote an implementation of ROAM". Great; anyone within the industry who codes can do an implementation of ROAM. There was a time when just having done this would demonstrate both your keen-ness and your skill (ROAM isn't trivial to get working properly). Nowadays, you need to be showing "ROAM with my own custom modification that does X" - X just needs to be something slightly different, so that I can see you not only understand the common-knowledge (ROAM) stuff, but at least try to experiment and add your own ideas too. Hey, I don't mind if your additions are pretty slow, nor particularly innovative, although if your additions are of a high quality, you'll really get me excited)
7. Professional worker, or newbie intern?. Previous experience is NOT the issue here; what concerns me is whether you have the maturity and the professionalism to work in a high-pressure environment. "professionalism" is definitely NOT "suit and ties" or "always being on time". Heck, sometimes I end up habitually late for EVERYTHING some days (knock-on delays); but I want to know if you at least phone ahead when you know you'll be late, and WARN the rest of us, as opposed to just sneaking in late with some excuse. Equally I want to be sure that when the shit really hits the fan on some code you're working on - perhaps we're going gold tomorrow morning, 9am, and you promised you'd have the installer working by then, and now its midnight and you've unearthed a load of new critical bugs - then you don't just give up, nor do you work flat out, hoping to fix it before anyone notices. Instead, you get hold of your manager, and let him know the situation, and then get on with one of the other two options above :). That way, your manager is able to prepare for damage limitation; if you fix everything in time, great, he's happy. If you don't, he steps in at 8:30am and prevents everything else from falling to pieces, and he's a hell of a lot more happy than if you didn't tell him until 8:59am!
That's all off the top of my head; sorry its a bit waffling. I'm not claiming you can answer all those concerns in a CV, but every CV gives an impression of the person, and people WILL make guesses of answers to those questions based on reading your CV. The more CV's a person gets, the more they will try to answer these questions from your CV before spending the time giving you an interview. Hope this helps. :)