I'm in college presently, and to get into the tech world, it's a requirement from where I'm sitting. Good candidates have multiple ones with big name companies\hot start ups.
Boo, that stinks. Personally, I think internships are bullshit unless they're having you work on genuinely interesting stuff like Google's Summer of Code. I must have been pretty lucky as I never had to jump through any credentialing hoops to break into the industry (That was in '05, pre-bubble no less. Didn't even finish college). If I were you, I'd pair up with a co-founder, come up with an idea, and apply to one of the incubators while you're still young. Don't waste your youth trying to impress HR drones. Or, if you want to look-before-you-leap, just "intern" at a less sexy startup (You'll learn the same stuff pretty much)
At Khan Academy, we certainly do our best to have interns work on "genuinely interesting stuff", and we put huge emphasis on good mentorship, more so than is probably possible with a remote program like GSoC. Here's a bit more info about our internship program: