Sponge, I've been wanting to post all day and am finally getting the chance. I know others have pretty much said this already, but it's totally natural to want a partner. Look at how many people get married, and how many dating sites there are. Pretty much everyone has the choice of being single if they want to be, but virtually no one chooses it - at least long-term.
I agree with others - wanting affection, intimacy, wanting to share things with others, etc, is all a part of being human. Yes, of course it's ideal if we can be happy on our own, and our self-esteem shouldn't depend on being with a partner. But that's a damn sight easier said than done, especially when you've been single for a long time.
OD (in my experience) constantly raises your hopes and then dashes them. Emotionally it can be very difficult. And, as you say, again and again you've had bad luck, and in my opinion it's natural to look at yourself and wonder where you're going wrong - I do too.
When I was 31 I broke up with a (lovely) boyfriend (or rather he broke up with me). I was devastated. Friends kept saying "oh, you'll meet someone soon". When I said I didn't think I would, they acted as if I was being whiny and negative. But sadly I was right - I was 38 when I finally had another relationship. It was a soul-destroying time which I think really damaged my self-esteem. All my friends were finding partners, having children, etc, and I felt so lonely sometimes. An active social life does NOT make up for the lack of a partner.
Sorry, I've rambled on for ages but just want to say that I think I understand a little of what you're feeling. I know everyone on here just wants to help, because you come across as awesome - you're intelligent, have so much empathy, you're funny, sparkling ... honestly, that's how you come across to me.
Big hugs ... and please don't go away.