This answer is outdated as of patch 2.0.1 - please see z's answer instead .
When you die, you need to wait a few seconds and then your character respawns in the last check-point or at the beginning of the current dungeon floor.
You respawn with full health, full resources (unless you're a barb), and in the same game state (so no monsters are resurrected).
If you died during a boss of mini-boss fight (purple name), however, you respawn in the checkpoint right before the boss and the fight is completely reset - the boss has full HP again.
If you are level 10 or above, you lose 10% of the current durability of each of your items.
gaming.stackexchange.com/users/122/Oak
As of patch 2.0.1, you are now given 3 options when you die (after a 3 second timer):
Respawn at your corpse Has a countdown of 5 seconds Limited to a total of 3 times within a short period of time Cannot be used during boss fights.
Seems to replenish a 'charge' once every 1-2 minutes.
Respawn at the last checkpoint Instant
No limit to number of times Respawn in town Instant
No limit to number of times
gaming.stackexchange.com/users/3917/l I
In Diablo III, dead players respawn at the last checkpoint they reached.
The good thing is that you no longer have to hunt for your corpse, the character will be wearing all the equipment and will have full health.
I don't believe there is any experience or gold loss upon death either, but seems there is loss in durability of an item
gaming.stackexchange.com/users/200/Sathyajith Bhat
Thankfully I have yet to die, but I did find this explaining death in Diablo 3 .
Hardcore characters are as they were in Diablo II;
mortal.
One death
there is the end of a character.
Forever.
For non-hardcore characters in Diablo III, death is a very temporary setback.
Dead players can be resurrected by other players on the spot, or after a few second delay they may choose to respawn at the last checkpoint they reached.
When they respawn they are wearing all of their equipment and have full health; there is no corpse to retrieve or loot as there was in Diablo 2.
Characters do not lose any experience or gold upon death... As noted in their sit-down demo at E3, the developers did mention having to pay a hefty amount of gold in repairs after wiping.
gaming.stackexchange.com/users/18818/Zero
When you die, and in a group.
Each party member can resurrect you by activating your grave/remains.
You can than select if to resurrect at that point, or resurrect at the last checkpoint (as stated before)*you still loose 10% durability if you are higher than level 10.
gaming.stackexchange.com/users/26725/Saariko
Diablo's first and second installments handled death differently, both in terms of exp\gold penalties and also in if you respawned or not or instead had to reload from an earlier point.  In Diablo III what happens when you die?
What happens when you die?
gaming.stackexchange.com
<diablo-3>
gaming.stackexchange.com/questions/66244
gaming.stackexchange.com/users/15095/Ender
You respawn in full health with full resources at your corpse. This is limited to a total of 3 times. In Diablo 3, when a players death occurs, there are few options presented, depending on the type of character.
Players describing the available options, regarding a players death.