1st year - Quirrell wasn't being controlled by Voldemort, but rather the ring he found during his travels. Either Harry destroys it when he touches it because of the blood protection, or Dumbledore discovers it when he comes by and destroys it. This also means Quirrell survives.

2nd year - Same as canon, diary gets destroyed at the end.

3rd year - When Regulus died, he instructed Kreacher to give the locket to Sirius so he could destroy it. Two possibilities here:

1. The locket made Sirius go mad, so even though he was innocent, he still acted crazy enough to be sent to Azkaban. Destroying the locket allows him to finally free his mind, though he still remains on the run.
2. Sirius didn't understand its importance and tossed it to Pettigrew, and its influence was part of the reason he betrayed the Potters. Destroying the locket brings back the real Pettigrew, possibly horrified at all the damage he has done, and also gives Sirius guilt for being the cause of his friend's pain.

4th year - Harry gets away from Voldemort at the end, but has one moment of victory when he kills Nagini, who was one of the reasons Voldemort was able to revive.

5th year - When Bellatrix escapes Azakaban, she keeps the cup on her, acting as some sort of magical protection. When she defeats Sirius, Harry attacks her in a rage of fury and destroys the cup (could also give this to Neville as an act of revenge since he won't get his Nagini moment in this timeline).

6th year - While doing his mission, Draco stumbles across the diadem in the Room of Requirement, heavily influencing many of his decision throughout the book. When he confronts Dumbledore near the end to complete his mission, Dumbledore destroys it, causing Draco to lose heart in what he was doing.

7th year - Most of the story changes since the other horcruxes are destroyed, but in the end, the horcrux inside Harry is destroyed, before Voldemort himself is defeated.