This goes for random events - like tonight, when I whipped out the point & shoot & grabbed some cute images of Zada - all the way up to (and especially!) - weddings. Granted, there's more pressure at a wedding since you're being paid to render the day in images...but those "gems" you capture are worth it.
When you take a lot of images, you're going to get a LOT of usable ones, a bunch of good ones, and some REALLY good ones (Again, this goes for weddings or just in general). In my opinion, of course. If you're Ansel Adams or something, you might get 1,399 stellar shots. Then again, I'm not sure I've ever seen him do anything but landscape/scenic stuff...
I think the key to getting those unexpected shots is - of course - being prepared, but there's also an element of not tying yourself down with "expectations"; you must stay open. Basically, I 'shoot now, assess later'.
Some shots might not look candid or unplanned; that's the beauty of them. A lot of times, I'll tell anyone BUT the people who have vested interest that the photo was serendipitous. For example, the parents of the little boy in the yellow flowers - unless they read this blog - will never know as they were desperately trying to call him back from the edge of the wedding gazebo (the bridesmaids/groomsmen were walking down together) I happened to turn and snap this shot of him. Can't lie, it's better than I'd have gotten if we were posing the kid :)
Another thing to keep in mind is don't always think "straight" - unless you're taking a scenic photo of the ocean, you don't NEED a straight horizon anymore. Shake it up a bit - be daring.
Of course, you can venture into the "too daring" category, which includes putting yourself (or others) in danger just to get that shot...I'm talking about hanging out of trees or cars in order to take a photograph. Granted, MOST of the time when I shoot out of cars, I'm not driving, but that's not always the case. However, in my defense, when I'm photographer extraordinaire AND behind the wheel, I don't focus/aim/compose; rather, I shoot and what I get is what I get. I.e., my eyes are on the road.
For the "desolate" shot (above) I was the passenger and I cheated a bit...straightened it a tad & turned it B&W...but who's to know if I'm not saying anything?
Ok, so for the Minneapolis Skyline shot, I was driving (hence the blurriness and horrible composition), but again, my eyes were on the road...no less so than if I was checking things out normally, anyway. All I'm saying is keep an open mind and you'll find you can get some pretty neat shots.