It depends on a lot of factors. If you're in a country where tuition is free, then it's more worthwhile than if you're in one where tuition costs 5 years worth of salary...
If you want to learn to be a programmer or artist, I would recommend a degree focused specifically on those professions (computer sciences, software engineering, fine arts, etc).
If you want to be a game designer, then maybe a game school is a decent choice, as there isn't a well agreed upon educational framework for that profession (yet), so game schools are the closest thing. Alternatively, you could get a tertiary degree in anything else too - English literature, Philosophical Theology, Psychology, Electrical engineering, Teaching, etc (if education is a luxury you can afford). The point of a degree, aside from starting a career is to create more well rounded adults, and people with lots of life experience tend to be good designers in every field of design (IMHO).
For what its worth though, game specific courses can be a bit predatory. Hopefully it's different in the rest of the world, but here in Australia, the local game schools produce an equal number of graduates per year to the number of people currently employed in the local industry... The local industry certainly isn't at a 100% growth rate -- so if we guessed 3% growth, then 97% of graduates have no hope of finding an employer... It's even worse than that when your realize that they are also competing against the people who did specialised art/code degrees, and people who didn't do a degree at all. To make that picture even worse, pure "design" jobs probably account for well under 5% of all game industry jobs, so the competition to secure an actual "game designer" job is fierce.
In that light, I would certainly recommend having a portfolio that proves you're worthy of such a rare career. Maybe that means skipping school to toil at a basement desk. Maybe it means doing a degree and spending nights and weekends on hobby projects. Maybe it means packing a tablet PC into a backpack and hiking across Europe...