Hmm. For once you have me stumped. I become as close as I want to be with people and, I don't really think (or realize?) there's a gap. Might be one of my personality flaws. I dunno. Are you talking about a romantic relationship or just creating a close friendship in which you can fully trust someone?
It seems being emotionally close with people is not so difficult for me. I've been told I'm very approachable/easy-to-get-to-know-and-share-things-with etc. A good number of people feel emotionally close to me. Interestingly, though I'm emotionally close with a couple of, to me, special guys -- it's my desire to go beyond the emotional stuff to a more intimate physical aspect and that gap seems not to be bridged as of now.