Having a mentor is good because it helps you establish connections in academia. It's always good to have a friend-of-a-friend that can help you out.
I found a couple mentors just by asking for advice. For example, I met my academic advisor as soon as I decided my major. I went to the chair of the department, asked him if he had a minute and said "I want to be a good student, any tips?" And it went from there. I regularly stopped by every couple weeks just to talk and he gave me advise on what classes to take, scholarships, REUs to apply for, etc.
I suppose many department chairs aren't as open as mine was, but it really doesn't have to be a chair. Start with one of your professors if you have to, start going to office hours sometimes. That's what I did for my research advisor. I had him for a "special problems" class, and after the class ended I continued to go to his office and ask about his research and if there was any way for me to get involved (if they say no... ask if they know anyone else)
As a result of this I got really good recommendation letters (they rang out more than "He got an A in my class") and was able to get into a number of top graduate schools.
Finding a mentor isn't really like finding a girlfriend or anything, it shouldn't feel like some kind of a commitment. I like the word "advisor" better because it's clearer what you should ask of them -- advice. It kind of evolves into a mentor-mentee relationship over time as they start taking interest in your doings. If it seems that they don't like to talk to you much or give advice... then they don't want to be a mentor! Just find someone else. Like I said, you don't have to commit to one person, and it's even best if you don't since you'll start building a circle of influence by building a "council of advisors."