Constantly, and have saved thousands of dollars over the years.

Hilton lets you do it on their website most of the time, just click to open the reservation, recheck the rates, if it's better click and you have the new rate. You can keep doing that until you check in.

If they won't change the rate for you, book a new room at the lower rate and cancel the old reservation. Make sure to do it in that order, don't cancel and try to book and find out in those seven seconds the rate sold out (done that).

Prepaid and other rates you can't cancel of course don't work so well for this.

But, yes, you should always check your hotel, air, and rental car rates.

There are threads in several of the hotel forums about rate drops.