Earlier this week there was a big feature on the UK MSN homepage about the value of a university degree. The central thrust of the feature was that a degree does not prepare you for the real world and leaves you only with an enormous debt and a huge hangover.
The article contained a link to a discussion where folks told tales of woe and how their hard earned qualification has not landed them the job of their dreams.
The way I see it (if you really want to know) is that if you decide you want some thing (such as the "job of your dreams") then you should plan a campaign which will get you it. A degree can be a useful part of such a campaign. But it is not the only one. You should find every other possible way to get there. Try to land some work experience in the area. Do things that broaden you out and make you more "interesting" to people working in the field.
If you want to be a games programmer, by all means do a degree in it, but also start writing little games and putting them on your games programming blog. Start contributing to forums about the field, asking and answering sensible questions. Get a job in the business, even if it is just working in a games shop. It all helps make you into a more enticing prospect.
Getting a degree and then expecting to be snapped up because of your evident brilliance will not work. In fact I don't think it ever did. When I did mine, all those years ago, when history was current affairs etc etc I remember being told that a degree is not a job ticket, but merely a licence to hunt....