PBR has nothing on the Pokemon Stadium series.
Despite that, the chances of another Pokemon Stadium game, unfortunately, are about as likely as a remake of G/S/C. It more than likely won't happen.
Kinda seconding KhaosKnight here. A GSC remake actually does appear to be rather feasible. There's nothing saying that it will outright definately happen (or not happen), mind, just a lot of things pointing towards it.
There are a million and one references to GSC in Diamond/Pearl (Mentions of Prof Elm, man who talks about Whirl Islands and other various GSC places/events, the SecretPotion, even an unnecessary appearance from Jasmine!).
Ingame coding that allows one to get Pokemon from Johto, similar to how Pokemon migrated from GBA games can come from Kanto, Hoenn, etc... only ATM there is NO way to get Pokemon from Johto into 4th gen games - unless there's a remake?
Plus, there's the fact that the Regis and the Kanto birds trio being available in Platinum, but a noticeable absence of the Johto legendary beasts trio in 4th gen games thus far...leaving the door open to another way to get them in 4th gen games maybe?
So it's not all that farfetched, actually - plus the potential for profit that could be made is certainly there given the amount of people who would probably buy a remake (like me :P ), a more major aspect that Nintendo would be concened with. But of course we will have to wait and see.
As for a Pokemon Stadium three... I kinda doubt it, really. Leastways not the name - they may make another PBR-type game along with some features from the Stadium games. IMO, PBR is kinda already the 3rd Pokemon Stadium - just without the minigames and whatnot (probably due to a different developer, methinks, in Genius Sorinity who made this game this time - also did Colo and XD), and with WiFi.