Well Rested

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

Fallout 3
The Well Rested effect is obtained by sleeping in a bed you own (in your 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, enables you to get 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 a bed you own (e.g. in your Lucky 38 presidential suite or Dino Dee-lite motel room) or sleeping with certain characters like Sarah Weintraub, Red Lucy, or Joana at Gomorrah.

Sleeping in The King's bed in his room on the third floor of The King's School of Impersonation grants the Well Rested bonus, despite not being an owned bed. (PS3: No longer true, possibly patched.)

There's also a queen bed in the bungalow in the last row of Jacobstown, which gives the Well Rested bonus when slept in.