Yes, God definitely created us for intimacy, and especially for intimacy with Him. Hence, the void in our hearts that can only be satisfied by Him.
I think men and women seek intimacy physically and emotionally. Though I believe that people who have a more worldly perspective view sex as part of that intimacy. Though sex has its own beautiful intimacy, it is more beautiful with the right person after marriage as we all know.
I will state that as a woman, I do crave for physical and emotional intimacy. I want someone who gets and laughs at my dumb jokes. Someone where we, as stated before, knows all my faults but still loves me regardless. Even more, to have someone who loves some of my flaws and is able to find beauty in them. I definitely miss having someone I can tell every single thing to and actually feel like they care and are just not simply trying to act like they care. I miss holding hands, cuddling and kissing. I miss those gentle yet settle physical gestures that tells me he loves me. Something as simple as when he glances at you from across the room in the middle of a busy night with guests would even be a gesture of physical and emotional intimacy.
I think intimacy is a beautiful thing. Really.