I personally believe the next would happen: 

Season 1: The town council, Jon and Isabelle get killed, which leads to Katherine not finding out about Elena and not coming to Mystic Falls. Tomb vampires also get killed.

Season 2: If Katherine does somehow show up, we saw her struggle with Vampire Elena, so I think Ripper Stefan and Damon kill her. Mason and the Werewolves get killed, so does Tyler probably. Would Trevor and Rose show up, idk but if they do Elijah does also, they probably end up daggering him like they did in the original timeline. 

Season 3: Since Isabelle is dead Klaus doesn't show up, at this point Stefan would be dealt with by Bonnie or he would threaten Jeremy and take her out. Since without Klaus showing up Bonnie would lack experience she would have in the original timeline, less powerful.

Season 4: Klaus shows up cuz of Stefan and breaks his curse, I see Stefan joining him since Elena and Damon would be together at this point. But with Jon dead no more Hybrids since Elena would be a vampire via Damon feeding her blood. Alaric would get killed by Stefan and he would take Jenna to Klaus for the ritual. Mikael is still in his tomb since Katherine is dead.

Season 5: Klaus and Stefan move on from Mystic Falls since Elena is useless to Klaus, let's say Hayley or some other wolf girl get's pregnant and the story moves on to New Orleans. At this point Rebeka is free and probably with Stefan who has his memories form 1920s.

Seasons 6, 7, 8 play differently without Sylas, Kai, Heretics, Rayna. 

Enzo would probably replace Stefan on TVD and he would end up with Caroline.

Stefan becomes a regular on The Originals. I assume he would get his Humanity Back at some point and return to TVD to apologize and probably move on like Lexi told him in Season 4 Finale.

If they never managed to contain Stefan during his binge in Season 1, how would the other Seasons progress and would some villains never show up?