I have a Darksteel Reactor on the battlefield, and my opponent plays Platinum Angel. How does the Reactor's effect resolve when it hits 20 counters with the PA in the battlefield? Do I win the game or not?
The game will be a draw. Darksteel Reactor will trigger, attempt to win you the game, and then resolve and do nothing (since you can't win the game). Once resolved, Darksteel Reactor will see that it is still in play and still has 20 counters, and it will trigger again.
603.8. A state-triggered ability doesn't trigger again until the ability has resolved, has been countered, or has otherwise left the stack.
This will continue without moving the game forward until a player removes either Darksteel Reactor or Platinum Angel or both. Since the game can't move forward, it is a draw.
Note: in a multiplayer game, "You win the game" is translated as "Each opponent loses the game." So if Player A had Darksteel Reactor, player B has Platinum Angel, and player C had nothing, player C would lose and players A and B would tie.
You will not win the game.
This rule is relevant here:
101.2. When a rule or effect allows or directs something to happen, and another effect states that it can't happen, the "can't" effect takes precedence. Example: If one effect reads "You may play an additional land this turn" and another reads "You can't play land cards this turn," the effect that precludes you from playing lands wins.
I don't know about the official rule system, but the "house rules" way I've always seen this played with my friends (who think draws are stupid) is that any persistent state that would cause you to win the game is effectively "put on hold" until Platinum Angel is off the battlefield (the effect doesn't retrigger until it can resolve differently).
So, if you put 20 counters on Darksteel Reactor, the game would continue, and if (before your opponent wins) you remove Platinum Angel while Darksteel Reactor is still down with 20, you win as soon as Platinum Angel is removed.