I too used to travel a fair bit on my own between 17-21 and stayed at a wide range of low to high end hotels, and never got hassled on account of age. I get the impression that the age restriction thing is probably more of a handy excuse if they get a bad feeling about you... if you look mature and responsible and unlikely to cause a ruckus, I doubt they'd turn down your money. Even better if you have a credit card.

As noted by some of the other posters, this may not apply to popular young-person destinations (e.g. Daytona Beach at spring break) where some places may rigidly enforce age minimums.

EDIT: Given that it has been over a decade since I was 21, I defer to Tide_from_PAE who says they apparently do ID now. That's a surprise to me... no one ever cared when I showed up at the Fairmont when I was 17.