Well I would say sex is important to most people, especially in relationships. When you have to do without, especially for a long time, it can be ...difficult.
Early in our marriage, my wife had a miscarriage. After that her "parts" never worked well. She was never...ever in the mood, and I'm not the type to force her, or guilt her into sex. I want to be with someone who *wants* to be with me. So our sex life sputtered to a stop. We've been married over 13 years, and we've maybe had sex 5 times in the last 5 years. None at all in the last 2 and half.
Sometimes it upsets me. Sometimes a lot. Sometimes I get mad, but I try not to show it. But I love her so much. I try not to think about it. We still love each other, laugh, snuggle and rely on each other. She's the one I love to tell bad jokes to, watch movies with, watch a sunset with, live with. She's my life and my love.
So how important is sex? I guess that depends on how much you love a person. With enough love I guess you can overcome anything.