The bonfires in Dark Souls fully heal the player, replenish their spells and healing potions, but fully revive enemies.
Step onto a Save Point in any game in the Kingdom Hearts franchise, and it'll quickly restore your HP and MP. The only real exception is Birth by Sleep, in which they only fill your HP; it doesn't do squat for your Focus meter or D-link gauge, though those are more like mini Limit Break meters.
Dragon QuestSave Points are the priests inside churches in towns. While these do not heal HP and MP, they do resurrect party members and remove status effects like poison and curse—although they do charge you money proportional to your level. In most of the games, this is the only real way to remove the curse status effect and remove any Cursed Equipment, as well as the only reliable way to resurrect party members until late in the game (the Trauma Inn won't do it, and the early resurrection spell "Zing" only works 25-50% of the time depending on the game).
Most save logs in Dubloon are located close to either trauma inns or red chests that replenish your crew's health and alcohol points. Ones that aren't are usually located somewhere within a dungeon.
In some games in the series, save points can heal, but they charge you money proportional to the amount of mana and health restored.
Digital Devil Saga: Large Karma Terminals do this. Small ones normally don't, but some Small Terminals might have a Life Terminal next to them to do the same job. (Small Terminals can also transport you to a large one if you need healing enough that you're willing to walk back.)
In Persona 3 Portable, the Save Point in Tartarus' first floor will do this, for a fee, which depends on your level.
Tales of Symphonia has a special ability that Raine (the healer) can use which drops the Mana Meter cost of all her spells to 1 while standing on a save point, effectively allowing a similar effect as this. Unfortunately, you'll probably want to use a skill that helps you in battle rather than a skill that helps you while standing on a Save Point, so unless you don't mind the micromanagement of swapping skills a lot this will see little use.
The save points in the Ys series heal you on approaching them. Some of the games also have trauma inns.
Pokémon Colosseum did this so subtly that it seems like it might have been an accident. PCs are used as save points, but they also provide opportunities to switch out the Pokemon in your current team, and newly-switched-in Pokemon are always at full health. Somewhat of a moot point for the most part, as virtually all PCs are either in a Pokémon Center or have a healing machine nearby.
In Lost Odyssey the save points don't heal you automatically, but loading a saved game does, so all you have to do is save and reload. Many — but not all — save points are nevertheless paired up with a healing orb, even though this ends up doing nothing but sparing you a quick reload.
The last level in the Subspace Emissary story mode of Super Smash Bros. Brawl includes save points that heal you and revive fallen party members.
First Person Shooter
Some inter-level checkpoints in Medal of Honor: Allied Assault do this, but most don't.
Hard Reset's checkpoints are almost always accompanied by jumbo-sized health and ammo pickups.
In Cave Story, most save points are next to heal points or beds.
Save statues in An Untitled Story completely refill player character's health aside from saving, which is nice since aside from beating bosses or collecting hearts (which are limited), there's no other way to recover health.
Some Sonic the Hedgehog games have the checkpoints reward you with rings, extra lives, or any other items, like shields, speed shoes, boost refills, etc. In games prior to Sonic Rush, you were required to have a certain amount of rings when crossing the checkpoints in order for them to give said bonuses.