I nursed my firstborn, a boy, until he was 16 months old. He lost interest at that point, perhaps because my milk either dried up or didn't taste the same, as I was about five months pregnant with baby #2, a girl.
I introduced solid food to her when she was about eight months old, and she gobbled up anything I gave her. I weaned her a few days before her first birthday, because I wanted to go on a women's retreat and not take her along. I still feel bad about weaning her before she was probably ready. By that point, though, she really was eating as much solid food as most 2- or 3-year olds, so I knew she would get adequate calories without my milk. However, she is the child that I have had the most difficult time understanding and bonding with. I love her dearly, but I just don't always "get" her or know how to get through to her. If I could do things over again, I would have nursed her much longer.
My 3rd child, a girl, turned 2 last month and still very much enjoys nursing. Sometimes I wonder if she's really getting anything out any more, since my breasts don't feel much different after nursing than before, and I don't usually feel the let-down of milk. But when she pulls away, she often has a trickle of white milk running down her cheek, so apparently, she's still getting something. She is a very sweet, compassionate, and thoughtful little girl, and I think that those qualities are at least partially attributable to the nurturing and tender care she receives multiple times a day through nursing. I love how enthusiastic she is about "mama mulk." It's pretty adorable when she hands me the Boppy pillow and says, "Mama mulk, now peeez. Boppy pillow!" How could I resist that? I'm not really in any hurry to wean her, although I do look forward to being able to wear normal clothes and bras again. Also, I'm pretty sure that at least part of the reason I haven't been able to lose the baby weight after being pregnant with her is that she is still nursing frequently, and for whatever reason, my body thinks it needs to hold onto excess pounds to make milk. I love snuggling with her, and breastfeeding is the only time she'll hold still (well, not really hold still, but at least she's pressed up next to me!). Sometimes if I'm nursing her while using my laptop or reading a book, she'll reach up a hand, turn my face toward her, pop off long enough to say "yook!" [look], and resume nursing. So I know it's not just that she likes the taste of milk. She wants connection with me. That's pretty special. That's why I'm still nursing her.