I think it is pretty easy to go the route of oh let's stop a hero from having that bad thing happen to them.
I have another idea though. Instead of say helping a Hero what if instead you went back and killed a villain before they could do the bad things. Initially this would good cause you prevented all the harm they would do.
But what if that villain had a special place in history. For instance what if you killed the villains that helped bring together the JLA or Avengers for the first time.
Then you could possibly have never had those teams form, and therefore when the big things started to happen it would be to late.
Another thing I can think of is if someone went back in time and killed Mongul. Then his son would have never trained Superman to be more effective with his powers.
Honestly, you could probably kill Darkseid and prevent god knows what. There are a few times when he's helped save the universe/multiverse, but he actually caused some of them himself.
Example: You could stop him from taking the Omega Force, let Drax have it. That would change the whole new gods dynamic for the better. Drax nearly signed a peace treaty with Highfather.
Take Alicia Masters away from NYC the day Surfer arrived on Earth. Without her there to touch his "human side" he wouldn't have stalled Galactus long enough for Johnny to return with the Nullifier and the Earth would've been destroyed. The universe would then follow of course because most of it's greatest protectors come from there. Adam Warlock never would've been created, Mar-Vell never would've become a hero, the Jean Grey never would've bonded with the Phoenix Force, ect., and that's all on top of the obvious repercussions of Surfer himself never being a hero.