This really depends. I have checked in at 5AM for the reservation on the same day without a problem. I would not, however, make this a habit. I would say that it probably helps if you have status with the hotel chain.

Once when I wanted to switch hotels in very early hour due to various service failures I thought that I would need to pay for both nights when I checked in at 4AM or so. I didn't know before checking out that I was only billed for one night.