A Cosmic Pat-on-the-back
Feeling proud of your children is the equivalent of a cosmic pat-on-the-back for a job well done. I am so proud of my children for the people they are that I could brag about them until somebody taped my mouth shut. There are very few things in life that you can point your finger at and say "Look, look! I'm responsible for that. I made that!" My children are my proudest accomplishment, and on some days I feel they are my only accomplishment.
I also love hearing people brag about their kids -- really! I do! Because, to me, they are telling me that they feel proud of the job they did/are doing as parents. And the world is a much better place with lots of good parents -- I try not to see it as a contest. Although I have to admit to the times I bit my lip to keep from one-upping, which is a natural instinct, I think.
The secret to successful bragging is to keep it short. A simple "guess what? So-and-so won a prize for whats-and-such," is hardly annoying if you leave it at that. The bragging target expresses interest because it is expected; it doesn't mean they want you to continue describing your child's greatness! Sometimes it is funny to watch the target's reaction to a brag. For example, "Hey, my kid scored in the 99th percentile on the ACT," can elicit the raised eyebrow response that indicates "really? Your kid?! You couldn't open a can of beans without a master class." When I sense that from someone, I usually quickly follow up with "yeah, well, he didn't get it from me!"
Most of all, it is important to brag once in a while about your kids because it shows them that you approve of them. And it embarrasses the crap out of them!
Hey, did I tell you that my daughter made the Dean's List last semester?