DH and I were together for 9 years and married for 5 before we had our first child (he was 35 when she was born, I was almost 29). We had made it known that we were not having children and by the time we finally had our DD, people had finally stopped asking when it was going to happen and were surprised. It was just a natural progression of our life and marriage. It wasn't a great longing by either of us, and I think we would have been happy had we decided to remain childless.
We said we would only have one child, and we meant it...at the time.
When DD1 was 22.5 months, we welcomed DD2. I had to talk DH into that one a little bit, but from the time DD1 was about four months old, I knew that we needed another kid. DH was happy with one, and it took almost a year of convincing to get him to try for another. In the end, it's been hard having two children because "have another one so they'll be best friends and playmates!" is a lie told by other parents to get you to suffer along with them.
Just kidding. Going from one kid to two kids felt like going from one kid to ten kids. But it's twice as rewarding.
The other day, DD2 fell and hit her ear off the coffee table (she's not quite 2). She is usually very stoic and doesn't feel pain but was crying a good bit. DH held her. I held her. Her sister walked into the room and DD2 goes "Harper, uppy!" and reached out because she wanted DD1 to hold her and comfort her. I thought I would die of love and joy and happiness that between all the fighting over toys and fighting for attention and running around destroying my house, somewhere in there is a love between siblings that I have helped to foster and nourish. Those single moments - that is what makes parenthood and having two children the best thing we have ever done.
I think being child-free is awesome. I was happy that way for almost 30 years. And I would still be happy that way if my kids had never come along. But I truly feel that the love you feel for your child is unlike any other love out in the world. The fact that sometimes I just want to smell my kids means I either love them more than anything else or that I'm mentally unstable. It's a toss-up.
Being labeled as "DD1 and DD2's mom" instead of my first name hasn't really been a bother to me, and I don't felt like I have lost my identity with becoming a mother. It helps that I have a full-time job and get to interact with adults on a regular basis. It helps that I still run and have been able to enjoy my hobbies, although on a smaller, not all-encompassing scale. I was able to train for two marathons last year, and that mainly involved running during my lunch break and only missing out on Sunday morning breakfast with the kids. Instead of watching tv, reading, or shopping, I hang with the kids. I don't need more crap to fill my house and daycare times two takes up most of my money, so I don't miss shopping. TV is watched when I run on the treadmill after the kids are in bed. I read less, but not too much less and having a longer commute means more time for audiobooks.
Edit: And I had my tubes tied after my youngest - I was 30 and my doctor never questioned me once about it. I said I wanted it and it was scheduled for a few weeks later.