I definitely think they can. One of my best friends is a guy I've known since middle school. There is NO sexual chemistry whatsoever.
If you start off a friendship have feelings for the person that you're supposed to be "just friends" with, I think that's when it becomes a problem. Staying "just friends" with someone that you have feelings for and watching them date others can be a really disheartening experience. I've been on both ends of the spectrum and neither side is fun. I really think that if you want a lasting friendship with someone of the opposite sex that it is important that both people NOT see each other as a potential boyfriend/girlfriend.
ETA:
And while some friendships tend to bloom into a relationship after a while, I can't help but think there had to be some sort of attraction from the beginning.
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