After reading some of the stories, I'm a little (but not much) swayed, so I'll say that it is possible. However, I really do think that 99% of the time, there is an attraction. For all of you who had friends of the opposite sex that you weren't attracted to, I can almost gaurantee that they were attracted to you and simply never said anything out of love for the friendship. It may not be the type of attraction where you're in love with the other person, it's probably a strong attraction to their personality (which I think is what creates strong friendships)
At least in my life, I've had and still have best friends who are guys, and usually I've got a crush on them and they don't know, or I find out they have a crush on me. Just because there's an attraction doesn't mean there can't be a great friendship.
Just my 2 cents