^ Agreed. Networking also works well. Send lots of emails with "Introduction- (Your Name)" in the subject line. Just say that you're a student, interested in the affairs of the company/organizations, and was wondering if there were internship opportunities available. Also attach a copy of your resume; couldn't hurt. You might be surprised.
Alumni and random contacts are also valuable resources. I once sat next to a gentleman on a train from Richmond to New Jersey; after chatting to him for a while, it turned out that he had done some high profile work for the DNC and chaired a presidential exploratory committee for a certain Senator. Networking doesn't always have to be done through structured events; strike up great conversations with interesting people, and then follow up with them via email! You never know who you might run into and how they might help you down the road
The thing about networking is to stay followed up. Don't let your contacts fade away. There are a variety of strategies for doing this, like arranging face to face meetings every so often, or just following up to see how the person is doing.