Healing over Time (HoT) effects
Heling over time effects are rare in D&D/Pathfinder compared to say, an MMORPG, but they do exist. They can be broken into 3 categories: Fast Healing, Regeneration, and Other.
Fast Healing:
Fast healing is an effect that represents the natural healing process, just sped up to an incredibly fast rate. Instead of taking days to heal, with fast healing you would typically heal in rounds. Fast healing is usually denoted by the words "fast healing" followed by a number. The number is how many HP you heal in a turn. For example, fast healing 1 heals 1HP/round. This means in one minute, you will have healed 10 HP. Fast healing 2, means 2HP/round, etc.
There are not that many spells that give fast healing in Pathfinder. It is mostly a monster ability. As others have pointed out, there is one called infernal healing which grants fast healing 1 for one minute. This spell is ok at level 1 for out of combat healing, as it heals more HP than a cure light wounds at that level. It does not, however, scale at all with level, since the amount and duration are fixed, so the spell becomes comparatively worse as you level up. The other downside to it is it has the evil descriptor. Repeated use of it can shift your alignment towards evil. Many GMs and campaigns do not allow evil PCs, so this could become problematic. The best use for this spell is on an item. A wand of infernal healing will cost 750gp, and will heal (assuming no waste) 50 charges X 10HP = 500HP. Compared to cure light wounds which only heals an average of 5.5/charge = 275HP. That said the cure light wand will heal faster, and that might matter in terms of buff durations, getting interrupted, etc. There is a greater version of the spell, which grants fast healing 4 instead of 1, but is a 4th level spell. Using a 4th level spell slot on this is not recommended.
As others have said, in 3.5 there are also the vigor series of spells (lessor vigor, vigor, greater vigor). Lessor vigor gives fast healing 1, and does scale with level, up to a max of 15 rounds. Vigor is a 3rd level spell that gives fast healing 2, and lasts up to 25 rounds. Greater vigor gives fast healing 4 for 35 rounds. Note that one of the issues with allowing both pathfinder and 3.5 content, is that there are some things that have the same name, but do something completely different. For instance, in pathfinder, the vigor spell exists, but it has nothing to do with fast healing, and is instead a cantrip that gives +1 on a melee attack roll.
Regeneration:
While fast healing is mostly described as accelerated natural healing, and can't heal things that natural healing cannot, such as a severed limb, regeneration is a more fantastical sort of healing that can heal lost limbs. Mechanically speaking, regeneration works the same as fast healing for HP gain (regeneration 1 means heals 1HP/round, for example), it also lets you re-attach, or even regrow lost limbs (re-attaching is usually faster than re-growing). The other huge benefit of regeneration, is unlike fast healing, you cannot die from damage while regeneration is active. For example if you had regeneration 5, and 14 con, and an attack reduces you to -14HP, if you had only fast healing you would die, but if you had regeneration you would merely fall unconscious. What's more, you would continue to regain 5HP each turn until the third turn in which your HP would be positive again, and you would wake up. Regeneration is a monster ability and is typically overcome by doing a certain type of damage, such as fire or acid, to the monster.
There are very limited ways for a PC to gain regeneration. Most of these involve shape-changing into a monster that has it. As far as I know there are no spells or items that give you actual regeneration (even the ring of regeneration is not true regeneration). There are however, spells that will shape-change you temporarily into regenerating creatures. Plant shape 3 and giant form 2 will both let you shape change into forms that have regenerate 5, which is very good.
If you are playing with monstrous PC races, such as a troll or something with regeneration, you could use the spell Transfer Regeneration to confer your regeneration to a different PC temporarily.
Other: Greater Path of Glory
I also wanted to mention Pathfinder spells that, in my opinion, are even better than the fast healing spells, and stack with fast healing and regeneration. As these spells do not mention regeneration or fast healing, they are technically neither, even though they effectively act like fast healing. These are path of glory (heals everyone in its radius 1hp/turn for 1 round/caster level) and greater path of glory (same but 5hp/round). These spells are good because they affect multiple targets. There affects for the first round work on any 4 adjacent squares, and on the second round and every round thereafter, you can extend this out to another 5 squares. This means that first turn you can affect 4 PCs, second turn up to 9, so larger parties get more out of them. If you have a lot NPCs or animal companions, mounts, familiars, etc, then this is even better because it heals them too. In fact, tiny familiars can share your space so they are even affected first round. Also, it only heals allies, so you don't have to worry about accidentally healing enemies with it. There are two ways to make good use of these spells, in combat (in limited situations) and out of combat.
Out of Combat
Usually these types of spells are pretty mediocre in combat (though there are situations that call for them), they really shine for out of combat healing. GPOG at level 10, assuming a party of 5, will heal 25hp total/turn, for 10 turns is 250HP (but in reality the first turn is only 4 squares big, so it gets 245HP across 5 targets, one target missing out on the first 5HP. If your party is bigger, it will heal even more, if its smaller, less). This is by far the best out of combat healing spell you can cast in terms of total HP healed (not including items). Another benefit of this spell, is you can cast other healing spells while its active, or use wands or potions. Since the amount is set and not random, you will know before it is even cast how many HP it will hela you and if you will need more. Therefore while you are standing in it, you can use other healing spells or even infernal healing (or vigor if you are allowing 3.5 content) since it is not technically fast healing so it stacks with it (though check with your GM as some GMs may count it as fast healing). If you have a wand of cure light wounds, for example, you can use that to "top off" healing on people standing in the path that will need extra. As the path tends to heal more HP/turn as the wand, and hits multiple targets, its a faster way to heal in between combats than just using the wand by itself, which can potentially make the difference between having your minute/level buffs up for the next fight or not. It also means less time for enemies to sneak up on you or prepare an ambush later in the dungeon.
In Combat
In combat GPOG is only really good if you have a very oversized party, are trying to keep NPCs alive (like your crew on a pirate ship that might get caught in the occasional AOE), or if you are in a very long boss fight in which all that HoT will add up if you cast it first round (assuming you already have all your buffs up and don't have any good nuke spells or spells that mess with the enemy to cast or none of them would be a good fit for the encounter). These are very limited circumstances.
Other than the above circumstances, the spells are also great for in combat healing if you have a celestial totem skald. The celestial totem skald's rage increases the healing on anyone in the party that accepts the rage by the caster level of the spell. So at level 10, that is 15HP/turn on everyone, making it combat viable. If you have skald's vigor, the skald will also gain some fast healing on top of that (as GPOG is technically not fast healing, even though it acts like it, so it stacks). Mind you although it works as RAW, not all GMs will allow this because it is very powerful and works based on a technicality (the fact that although GPOG behaves very much like fast healing, it technically is not). The one campaign I know of with a celestial skald using GPOG, the GM has ruled that the bonus healing from celestial totem only works on the first round. Even still, he has used it to great effect both in and out of combat.