Well Rested

Well Rested is a status effect that grants the player character a +10% experience boost for 12 hours after sleeping in an owned bed in Fallout 3 and Fallout: New Vegas.

Fallout 3
The Well Rested-effect is obtained by sleeping in an owned bed (in the Megaton house or Tenpenny Tower suite, a rented bed, or a cot in Kenny's Cave).

The perk Deep Sleep, available with the Broken Steel add-on, allows getting this status by sleeping in any bed, but only for 8 hours.

Fallout: New Vegas
Like Fallout 3, the effect is obtained by sleeping in an owned bed (e.g. in the Lucky 38 presidential suite or Dino Dee-lite motel room), safe house beds, sleeping with certain characters like Sarah Weintraub, Red Lucy, or Joana at Gomorrah, or specific queen beds in certain locations (such as Jacobstown bungalow).