Generally depends. Early dumps are usually the result of an early sale or people getting their hands on a copy way before the street date (like employees or the like). For normal sites, it would probably be at the end of the day by the earliest, and a couple of days normally. It takes time to rip the ROM, make sure it's perfect, and then submit it, then for sites to actually get around to uploading the file or splitting it if necessary.
As stated earlier, some people got the game early today or even before then, so as we speak the game might be getting online. Just be patient, those who pay have the advantage of time over us freeloaders. ;P
Edit: That all was in response to Raestloz, didn't feel like quoting because I thought I'd get it in before someone else posted. XD