Resting

Resting is used to heal in a safe place without the need to use stimpaks or healing skills. The player is unable to rest if there are enemies nearby, the player is being irradiated, or if the bed is owned.

Fallout and Fallout 2
In Fallout and Fallout 2, you can rest in any place, as long as you're not in combat, using the Pip-Boy 2000 alarm clock function.

Fallout 3
Beds are used to heal completely by sleeping. You can not sleep in an owned bed (if the owner dies the bed won't revert to an unowned state). Many places have unowned beds for players to use freely. Sleeping for any amount of time in a bed will heal your health and any crippled limbs, but will not get rid of any rads you have accumulated. You will not recover health from selecting to sleep but then canceling.

If you wish to pass a period of time but there is no bed nearby, you can wait for up to 24 hours. This allows you to use shops that are closed at certain times or pass in-game time for any other reason. Health is not restored as it is in sleep, and you cannot wait while you are being irradiated or if there are enemies nearby.

Well Rested
If you sleep in a bed you own or rent (such as in your Megaton house, Tenpenny Tower Suite, Kenny's Cave, or a rented room) for at least 8 hours, you will become "well rested" and gain a 10% bonus to experience gained for 12 hours.

However, there is also a Broken Steel-added perk that becomes available to you at level 22, called Deep Sleep, which allows you to earn the well rested bonus in any bed you choose to sleep in (provided the bed is not owned and the area is safe).

Bed Locations

 * The article Fallout 3 player housing provides numerous locations with "free beds".

Hotels
Sleeping in these will provide you with the "Well Rested" bonus.
 * Megaton, Moriarty's Saloon, Nova, 120 caps.
 * Rivet City, The Weatherly Hotel, 120 caps.
 * Underworld, Carol's Place, 120 caps.

Add-ons
The Point Lookout add-on provides an additional well rested bed in Kenny's Cave, provided you pass a speech check, have the Child at Heart perk, or retrieve Kenny's special teddy bear.

Fallout New Vegas
Beds will heal a player completely unless the player is in Hardcore mode.

Goodsprings

 * The bed in the gas station is available, if Ringo isn't already sleeping there.
 * The bed in Victor (the Cowboy robot) is also available.

Mojave Outpost

 * Unoccupied bunk beds in the Barracks are available.

Misc

 * The cots in the Nevada Highway Patrol Station (between Primm and Mojave Outpost) are available.