A Relationship Without Sex

How important is sex to you? Is it so important that you wouldn't be in a relationship without it? Let's just say you met someone and you all had an instant connection, everything with them was great, but for whatever reason whether it be by choice or force he/she is not having sex. Would you continue the relationship or end it? I think that we have begun to put way too much emphasis on sex and it's importance. I mean of course sex is important, it is how we reproduce and is definitely ONE major form of intimacy, but isn't the ONLY form of intimacy. Not every kiss, hug, or touch has to lead to  sex. It IS possible to have a successful relationship without sex. But what are your thoughts? Could you be someone who wasn't sexually active?