That's what I usually do, too, but they also ask that I sign off and drop something in the express check-out box. Which I've always done. But judging by everyone's answers I guess it's not necessary, though.

I ask because, one time I got a call from the front desk asking me if I was ready to check out yet. It was 10 AM and I had already arranged to check out at 4 PM. Then I got another call an hour later asking the same thing. So, I was just wondering if the hotel is really inconveniced if you don't actually inform them that you are checking out. I usually leave quite early, though.