It varies by class and by HP system. Rolled? Die-based average +1 ?
In 4e, a Paladin started with 30 and gained 60ish by 10th level, putting them at 90, only 3x as much.
In 3.5 a fighter started with 10 and on average wound up with +50 by 10th level, total of 60, but 7x as much(not including Con mod, say, 2-3), including con mod for another 25ish HP, rounding their total out to 85-90. Making their final HP almost 10x as much. If we use full-die+con mod we're looking at +125 for a total of 135, 13x as much.
Though the numbers didn't change vastly between 3.5 average and 4e, the multiplier certainly did. Personally I think a larger amount of health at lower level and a slower HP-pool advancement by 10th level is the way to go.
Perhaps not as much as 4e to start though. I would give everyone 10+1lvl of class HD+con mod. The average fighter/paladin would sit around 20, while the average wizard would be around 15. As the levels progress, I favor a Class HD+Con mod system(I mean, we need to make con realistically useful over the long-term). Giving heartier classes an average of 7-8 points per level, and weaker classes 4-6.
We'd still wind up with about the same totals, tougher classes would sit between 80 and 90, while squishier classes would sit around 50-70. I think those are good numbers for their respective classes throughout all levels between 1 and 10.
ADDITIONALLY: I don't know if I feel a lot of variant HP rules should be in Core or not, but I wouldn't mind HP(and general stat) multipliers for say, multiple tiers of pay, "gritty" @ 0.5x, "normal" @ 1x, "heroic" @ 2x and "epic" @ 3x, allowing of course for the DM to adjust those numbers as they want(say, maybe 1.25x or 1.75x). Just something simple telling GMs to consider the style of the game they want to run, and adjust HP accordingly.