As far as I'm aware, in most companies, videogame designers aren't just parachuted in as pure designers with no responsibility for anything else. Usually what happens is that a programmer or artist who demonstrates skill in that area is given responsibility for leading design on a game..they become game designers in effect. We're not yet at the stage where most companies are looking for pure game designers. The point is, decent game ideas are a dime a dozen, and there is competition within teams (between programmers, artists etc.) to get their ideas into the ring and have a chance of getting them either put into an existing game, or have a game made around it. You can bet a lot of programmers go home and spend a good bit of time honing their own pet ideas. So that's your competition. This might change going forward, and as roles become more defined, but installing game designers from other disciplines does seem to work fairly well, in that if you, for example, get a programmer and hand them the creative reigns, they'll have strong experience of what's feasible and what's not feasible in a game etc. and they'll know how the system works. If they can refine and communicate their ideas as well as a "game designer", then...?
We might get to a stage where most companies are recruiting pure game designers with no technical background or no background in any other games discipline. Particularly for certain types of games, perhaps ones that are heavily linear or plot driven. A lot of ads I've seen looking for game designers, though, talk about the position suiting someone from another discipline looking for more creative responsibility or whatever.
I should say that some companies DO recruit pure designers! Usually, however, they're looking for people with experience, who've already designed games etc. So the question is, how do you become a game designer in the first place to get that experience..and so on. A lot of companies still don't directly recruit designers externally..you'll see their ads for programmers, artists etc. but none for designers and the reason why is, they let designers emerge internally from other disciplines. Like I say, that may change..
All that aside, the types of subjects you'd be looking at when it comes to game design would be things like literature, history, film, art, immerse yourself in pop culture, English (you need EXCELLENT written and verbal skills), and of course, games. Play lots of games. Both videogames and others (board games etc.). Teach yourself about logic, reward. Also, psychology is a good one..things like human motivation, desire, appeal etc. It's good to know what turns people on at a fundamental level.
Personally, I'm approaching it from the technical-to-creative route, if I go that way at all. I'm doing a software degree at the moment, but I've an avid interest in game design, so I'm keeping that option open to me in the future. It's relatively easy to keep it going as an interest alongside college work.
There's also the difficulty of finding a specifically relevant degree qualification for game design..there are some dedicated courses emerging, but their relative quality and usefullness is questionable. I know some game companies that won't even look at graduates from dedicated games courses, although some are establishing themselves (a couple in scotland are the oldest, and probably the best, though they are more related to technical development than design).
edit - I forgot one more direct route - becoming a level designer is a good stepping stone to becoming a game designer. Testing -> Level Design -> Game Design seems like a sound route, but I think you might be looking for something slightly more direct.
