Text (FE+errata): {Tap}: Add one mana of any color to your mana pool. An opponent gains control of ~this~ at the beginning of the next end step. [Oracle 2009/07/08]
Only changes controller at the end of a turn in which it was tapped for mana. It does not change controller if it is not tapped for mana. [Duelist Magazine #4, Page 7]
You choose the player to give it to at the time it is tapped for mana. [D'Angelo 1995/07/07]
Will not change if tapped by Mana Short since Mana Short does not tap a land for mana. [D'Angelo 1995/03/22]
Does change controller even if it stops being a Rainbow Vale before the end of the turn (by effects such as Phantasmal Terrain or Blood Moon). The control change locks in when you announce the effect. [Duelist Magazine #8, Page 51]
If under a player's control due to some lasting effect, it will still switch players when tapped for mana. [WotC Rules Team 1994/12/15]
Stays in the same tapped/untapped state it is in when it switches controllers. [D'Angelo 1995/07/07]
If more than one player manages to tap it for mana in a given turn, then two control changes will be scheduled for the end of the turn. [bethmo 1995/07/19] These abilities resolve using the standard order for such things, so the current player's abilities are put on the stack first, then the opponent's. [D'Angelo 1995/07/25]
The land's changing of controllers is a new effect each time it is used so it will take precedence over any other control effects. This means that using Conquer on a Rainbow Vale won't guarantee that you keep it. [Duelist Magazine #7, Page 98]
Extended tournaments (see Rule 913) have banned this card since 1999/10/01.