Special encounter

Special encounters are special random encounters often unique compared to more common encounters which may consist of hostile non-player characters. They usually serve as entertaining points of humor, though some are very dangerous (mad brahmins), while some grant access to unique, sometimes powerful loot (Bridge Keeper). Most of these encounters consist of humorous pop culture references or other games or even earlier Fallout games (The Cafe of Broken Dreams).

The equivalent of special encounters in Fallout: New Vegas are done by the Wild Wasteland encounters if the player has the Wild Wasteland trait, which adds (and in some cases changes) random encounters and locations with similar humor of special encounters.

Fallout, Fallout 2 and Fallout Tactics
Some special encounters can be revisited; a map circle the same size as minor locations such as Toxic Caves and Golgotha appears on the World Map where it was found. If you leave the encounter and the map location is named "Unknown", the location is in flux; the encounter can be 'rolled' again, making a new map circle in that map location. If you want to 'lock down' a map location and display its name, reenter it. The exception is the 'Cafe' location, which will be 'rerolled', its location moving to the new encounter site, even though it has been named. Map locations where an encounter was declined will of course be marked Unknown.
 * There is a minimum level for each special encounter, to receive it.
 * Rarely, map encounters that would normally leave a map circle, do not.
 * Both, encounters that leave a map circle, and those that do not, will have to be reactivated in another map area once you decline to enter them. The game keeps track of this location, and will not spawn this encounter there again.
 * Unlike running out of fuel for the Car on map squares with a City circle in them, the "Out of Fuel" circle will be accessible properly if it is near a random encounter circle, even the permanent ones.
 * Rock collectors wishing to take their collection to the next level may find a single rock in all of the special encounters other than 'The Cafe of Broken Dreams'.
 * If you get the Explorer perk, you will obviously get more Special Encounters, but that includes 'bad' ones such as 'Toxic Waste Dump'.