I just finished college. My fellow grads and I have been thrown into a huge transition, whether we want to accept it or not. This is a time where we are seeking advice, information and guidance on how to make decisions regarding finances, insurance and all those fun adult purchases. While we may be broke now and for the next few years, soon we'll be making significant purchases (cars, homes, kick-ass TVs) that I doubt brands would want to miss out on. I want your brand to be my friend.
Who's missing out?
Apple and the PCs -- These companies welcomed us with open arms as freshman offering student discounts and handing out free iPods (and Zunes?). We got frequent deals throughout college because we were poor students. But now what? Acknowledging the next transition might be the simplest way of saying let's be friends for life. It could be as simple as suggesting podcasts that give career tips or as extensive as email blasts about the benefits of Apple for small businesses.
TCF Bank (or other campus bank) -- U of M students are pretty much forced into getting a TCF Bank account during freshman orientation. They should be doing everything they can to keep grads as customers as they start to want and need more banking services.
Amazon -- I would be surprised if their sophisticated user data didn't know that I had purchased textbooks at least once per year for the past four years. While it might not be totally accurate for everyone, serving up recommendations for books that help me handle life after college (new job, home decor on a budget, M-word books) are likely to be well received.
Car insurance brands -- I've received the good student discount for the past eight semesters and now I'm kicked off because I'm graduating. But why aren't they scooping me up as an individual account? I have no idea what insurance to buy but if they presented me with a recent grad package I'd sign immediately.
And someone who's doing it right:
Mint.com -- The Financial Fitness 'game' helps users learn about their accounts and explore the options of savings and investment. It's perfectly targeted to help grads get their student loans and budget in check.

Any other brands that you'd want to be friends with upon graduation?