It probably depends a lot on where you live. My wife's bike got stolen and she was woken up by police coming to check on it (one of the maintenance guys at our apartment noticed a man at 7-Eleven riding it and recognized it; came back running to check if it's indeed missing and called the police). We fully expected the police would do nothing about it (it was the cheapest Walmart bike), but an hour later they called that they found the bike and have the culprit in custody. It did help that the bike was a girly mint green with a wicker basket, so they instantly recognized it when they saw it.

Then again, in San Francisco, when my wife got her car window smashed and wallet stolen (she was late for class and dropped her wallet under the car seat, didn't stop to take it; but it wasn't the wallet that caught the thieves' attention, it was the breast pump bag that looked like a laptop bag; they threw it on the floor when they saw what it was), we never heard anything back from the police.