I recall that when I worked in hotel business, we overbooked all the time. Given the fairly generous cancellation policies and thus frequent cancellations it didn't typically lead to problems but from time to time it did - especially in high demand properties at high demand times.
The thing was that you couldn't get away with not doing it because if you have empty rooms on a big night with high rates there's going to be questions asked.
In terms of bumping people, it made a legit difference if someone contacted the property to announce a late arrival. It didn't guarantee the room but it certainly solidified the reservation. If the property hasn't heard from someone by 11 or midnight-ish, they'd assume a no-show if not otherwise announced. Doesn't matter if there's space but if you have next to no space and there's a guy on location willing to pay essentially whatever you ask (what choice does someone looking for a hotel room at like midnight in a booked out city really have?)..well you're gonna take that chance.
In terms of re-accommodation, agreement had to be gained. That means, if the guests nixed a hotel proposed by us (i.e. a dump an hour outside town), we had to go back to the drawing board. At first you'd obviously try your own properties and reasonably priced alternatives but if that's a no go, you'd typically up the price cap with every 15 minutes or so. In a few cases, people who had booked a pretty no frills room ended up in a high-end luxury property. Not the desired outcome but it's the risk taken.