When characters gain a hit-die, they reroll their hitpoints and keep the new total if it is higher than the previous one.
I like rerolling per session or adventure and have it represent healing as well.
In the dungeon-delving game I play in we re-roll our HD before each expedition.I am planning to use the same gaming system (a Hungarian mash-up of OD&D and B/X D&D) in a wilderness-based campaign, and I intend to have the players re-roll their HD daily.
We always did it with 1E/2E that you rolled a HP die and added it to your total when you gained a level. One campaign I had special trainers for leveling up that cost more but you would get maximum HP from the roll instead of rolling. Everyone pretty much used them. As for monsters, I've done average HP or max HP in those campaigns. I didn't usually roll HP because it seemed stupid to have some 4+1 HD Ogre end up with 8 HP. I ran a campaign where we rerolled the entire HP when you leveled up, taking the better of the two (old or new). This resulted in slightly higher than average HP totals. For monsters, I would roll the total and then if it seemed low, I would remove a die and roll again to see if it were any better. It's what would have happened if I had rolled for 1 HD and then 2 HD and so forth. I rolled all those monster HP. Now in this 1E campaign I have them roll HP as in my first example, no special trainers, and I roll monster HP once per monster also. I think that's how it's supposed to go, unless you have some special monster encounter with an especially beefy Ogre with 6 HP/die or something like that. I don't know what I prefer. I think rerolling the whole HP each level made the PCs tougher and if you don't do it for monsters you're shortchanging them.
No rolling at all, but calculated. In Echelon it is (level+BAB+Con)*(tier) [with Con ranging from 1..9, not 3..18].In D&D I ended up basing it on the Hit Die. Originally I did half-plus-one (Wizards got 3 hit points, fighters got 6) but that really underemphasized the Hit Die (that was supposed to be so much a justification that 'Fighters are tougher than Wizards'). Eventually it became Hit Die - 1:Wizards: 3/levelRogues: 5/levelClerics: 7/levelFighters: 9/levelBarbarians: 11/leveland it worked out pretty well.