In Star Trek: TNG "All Good Things", Picard bounces around time. Why doesn't the crew in the "real" time him taking them to the Devron System instead of to Farpoint Station, and why doesn't the future crew (Data, Geordi, Worf, Beverly) remember him taking them the Devron system twice before in the past, even though this anomaly seems to be able to affect the timeline (in other words, it doesn't seem like these are actually separate universes [if one simply considers the series])?
Because it probably didn't actually happen... sort of.
At the end of part 2 of the episode, when Q and Picard are having a chat back in the courtroom, Q appears to indicate that this was a test that was imposed onto Picard as a representative of humanity. Note in the dialog that they are mostly talking about Picard specifically and not anyone else.
(Picard is sitting with his head in his hands)
Q: The Continuum didn't think you had it in you, Jean-Luc, but I knew you did.
PICARD: Are you saying that it worked? We collapsed the anomaly?
Q: Is that all this meant to you? Just another spatial anomaly? Just another day at the office?
PICARD: Did it work?
Q: Well, you're here, aren't you? You're talking to me, aren't you?
PICARD: What about my crew?
Q: The anomaly. My crew. My ship. I suppose you're worried about your fish, too. Well, if it puts your mind at ease, you've saved humanity once again.
PICARD: Thank you.
Q: For what?
PICARD: You had a hand in helping me get out of this.
Q: I was the one that got you into it. A directive from the Continuum. The part about the helping hand, though, was my idea.
PICARD: I sincerely hope that this is the last time that I find myself here.
Q: You just don't get it, do you, Jean-Luc? The trial never ends. We wanted to see if you had the ability to expand your mind and your horizons. And for one brief moment, you did.
PICARD: When I realized the paradox.
Q: Exactly. For that one fraction of a second, you were open to options you had never considered. That is the exploration that awaits you. Not mapping stars and studying nebulae, but charting the unknowable possibilities of existence.
Here, Q explicitly admits that the Continuum wanted to test humanity as a continuation of the trial from the original TNG episode "Encounter at Farpoint". Since Q has a particular interest in humanity, and Picard in particular, he is directly responsible for what happens to him. So the fact that this experience is unique to Picard is probably also part of Q's doing.
Additionally, also consider how the Enterprise first encounters Q in "Encounter at Farpoint". Despite it being the origination of the Q Continuum's trial of humanity, it's an entirely different affair. He pauses reality and transports the available senior staff into his courtroom. Additionally, Q decides that Farpoint Station would be a good test for the Enterprise as a representation of humanity. With Picard in charge of the Enterprise, this responsibility largely falls onto his shoulders anyway.
In "All Good Things...", the only person Q affects or even talks to is Picard, seemingly having decided to cut out the rest of the crew from his little test. This also seems to indicate that Q arranges it so that Picard specifically represents humanity in this second part of the on-going trial.
There's a highly voted answer on a related question that also mentions these events happening specifically to Picard. While there's still plenty of uncertainty here (both timetravel and Q are confusing enough individually, and we're dealing with both here), I think it's more likely than not that all of the events in the episode specifically happened to Picard and no one else. In Picard's reality, he lived through these events and saw just one possible future. But in everyone else's reality, they never happened and nothing in their pasts really changed... but hopefully their futures will be different and for the better.
Now, what would have happened had Picard not realized the Paradox? There's no way to tell from the episode. But I could imagine a courtroom scene with Picard and his senior staff once again, Q references some evidence that he claims Picard provided (with Picard having no memory of the events from "All Good Things..."), and then Q enforcing whatever punishment he had planned originally 7 years ago. Or... assigning some other situational test to Picard that he'd find highly entertaining. After all, Q has to keep himself amused somehow.
(Really the name says it all. Godly powers. Mischievous, arrogant, and curious to a fault. I only added this note to have enough characters for an answer. Logic flies out the window in the presence of Q.)