I can't say for all genres but in science fiction and fantasy a new author has traditionally received $5,000 - $10,000. This has been confirmed over and over again by a number of places but the one I'll point you to is
Tobias Bucknell's survey (which I believe occurred in 2005).
I'm actually doing a survey right now and while I'm still collecting data it confirms that.
I will say that my debut contract was MUCH more than this (six-figures for 3 books) but a lot of that was because of my prior self-publishing success (I suspect) and a realization on the publishers part that if their advance was significantly lower than my self-publishing income I would turn it down immediately).
I've not heard of the "no advance" aspect that was listed earlier in this article, but I do have some very relevant data in that I'm negotiating my second contract right now. I was originally offered the same (on a per book basis) and the publisher cited "which is really good considering advances are about 50% these days). I didn't take it and we are currently in negotiations, and they have raised the advance considerably over the initial.
I'm not sure how much a single data point is worth, but it's at least better than nothing.