From Diablo Wiki
Resurrect is a way to bring other player characters back to life in Diablo 3. How this feature will work has changed repeatedly during development, and may change yet more. There are minimal (or no) death penalties in Diablo III, and dead players can choose to self-resurrect at the last checkpoint they reached, or wait for another player in the game to resurrect them.
Resurrecting another player required a resurrection reagent in early testing, but as of February 2011 no reagent of any type is required.The topic was revisited in February 2011.
 Death and Resurrection
When a player dies in Diablo III, a grave post appears where they perished. The dead player sees a five second countdown timer. Once the timer hits zero, they can choose to resurrect (with no death penalty) at the nearest checkpoint. Alternatively, the dead player can wait for another character in the game to resurrect them.
Living players have the option to resurrect a dead one, but only within a few seconds of the time of their death. It's not known if the live character must be within some set proximity to the dead in order to resurrect them, nor if there are other limits; monsters in the area, time required to resurrect, etc. There are no reagents required to resurrect; no scrolls or elixirs or anything else; characters simply click a pop up option upon another character's death.
 Resurrection Scrolls
The developers of Diablo III experimented with various Resurrection reagents during game development, including Resurrection scrolls, but ultimately determined that the ability to resurrect other players should not require any sort of potion or scroll. The ability to resurrect is directly implemented into the game interface, and does not require any items to use.
- Co-Op resurrection mechanic getting changed up. No more reagent. -- Diablo
- Yeah it’s [resurrection] always been instant, the reagent was removed for other... requirements. Which may change, so we’re going to keep that a secret for now.
The topic was revisited in February 2011.
- Will you be allowed to resurrect your team mate in Arenas? If not, are resurrection potions still in the game for regular play? --NocturneGS
- No reagents for resurrecting friends in co-op, instead there’s a short window of time to click on them or they’re running back. --Diablo
By "running back" @Diablo refers to the self-resurrection method, which allows dead players to respawn at the last checkpoint they reached, which is usually 60 seconds or less from the spot of death (assuming the dungeon between has been cleared of monsters).
It's not known if there are any limits on resurrection; must a player be nearby? On the visible screen? Can it be performed if there are monsters in the area? Is there any limit on how many times resurrection can be performed? Are freshly-resurrected players returned with full health?
 Resurrection in the Diablo Series
 Diablo I Resurrection
Resurrection scrolls were a part of Diablo I, where they worked like any other scroll. When another player died in the game, a living character could stand near the corpse, right click on a resurrection scroll, and then target the corpse with the resulting cross-shaped cursor. The dead character was instantly resurrected, but since all of their items had dropped when they died, they were in a perilously state, and needed quick fingers and a clear area to survive long enough to reequip and rejoin the fight.
Corpses in Diablo I could only be resurrected if the player had not yet chosen to restart in town. Once that option was selected, their corpse vanished and there was nothing for a character in the dungeon to do to resurrect them.
 Diablo II Resurrection
Resurrection was present in the developmental period of Diablo II, initially from scrolls just like in Diablo I; later as a skill only the Paladin could cast. One of his skill trees in early builds was devoted to healing, curing, and restorative abilities, and one of the highest level skills was Resurrect.
During development the Paladin's healing skills were largely removed from the game, or changed into Auras, and Resurrect was taken out entirely; for the Paladin and for anyone else. That game feature might go the same way in Diablo 3, though that seems unlikely with it still in place in early 2011.