Hit Die Heresy
While this is okay in certain campaigns, like my Mything* D&D campaign, where the characters are approaching the status of epic heroes, or my Dark Incarnations Star Wars d20 game, there are other genres where having more hit points than a roided-out elephant takes something away. That guy with the gun isn't a credible threat if the gun does 2d6 and you have 80 hit points. Even a maxed out critical hit would only do 24.
Another system, RoleMaster solves the HP dilemma with a highly ransom system that includes instantly lethal critical hits. If that goblin with a dagger rolls lucky, your 200 hp dwarf is dead. While this is certainly more realistic, it can make players with high level characters more afraid to take chances.
What I'm leaning towards for the next d20 system campaign I run is to give all characters their Constitution as their base hitpoints with a hit point bonus determined by class and level similar to the way Base Attack Bonus, Saves Bonuses, and (in non D&D) Defense Bonus are determined. I haven't settled on the exact amount yet... I am leaning towards the equivalent of 1 (old) hit die per 5 or 10 levels.
So a 10th level fighter with 16 Con would have:
Under D&D (assuming the old max hp for 1st level) he would have an average of 90hp with a max of 130 hp.
Under the HP Bonus system he would have 26 hp if I used 1 HD/10 levels or 36 if I used 1 HD/5 levels.
At 20th level:
D&D - an average of 175hp with a max of 260hp.
HP Bonus - 36 at 1/10, 56 at 1/5.
Now, this probably wouldn't be feasible for an actual D&D campaign... a 10th level wizard's fireball averages 35 points of damage. But in genres where the ability to deal damage does not ramp up with levels, such as Modern d20 campaigns, this might prove a viable alternative.
I should note, I did not think up this HP Bonus thing myself. I think I read it in Unearthed Arcana.
* No relation to Robert Asprin's Myth series.