While on the honeymoon my wife and I took a few opportunities to paddle around the hotel pool and every time it occured to me AFTER getting out to dry off and head back to our room that I had all kinds of knarly scars all over my chest, not just the big zipper down front, but a number of marks from drainage tubes and a "horrible" looking scar from a thorachotomy when they cut me open under my right arm to patch up some internal bleeding. Plus I had some pretty huge bruises all over my torso (they're still there actually, though slowly getting lighter by the day I suppose.)
It was the only time I really got "self-concious" over my scars, just wasn't sure other people wanted to see that kind of thing... Kind of a funny reason to cover up I guess.
They are a badge of honor, a sign that I've been through something REAL hairy and have lived to tell the tale. No one really asks to hear about it of course, but that's OK.
I get more of a reaction though from the constant ticking than I do from my scars. I also pick out scars on other people and sometimes start up "war stories" with it. Most of the folks I've seen that have zippers have them from by-pass surgeries of one sort or another so when they hear my tale, they're kinda beside themselves, "Man, and I thought I had it bad..."
I think if you have surgery before you're teens you really don't think of the scar at all and get self-cooncious about it. If you have your surgery during your teens and into your 30's, you'll probably be "concerned" about it, though it depends on how much you're concerned about your appearance in general. If you're a prima donna and you're going to have valve surgery, maybe you should line up an appointment with a plastic surgeon afterwards...
The rest of us? Yeah, it crosses your mind. It's there, there's no real hiding it, but in the end it's really just a sign of your life continuing. You went through something that most folks never consider and you're still kicking around, trying to pick out stuff that doesn't have too low of a cut in the neck. That seems better than the alternative...