So, what makes a good story about a former villain turning hero? Sometimes the reasons seem weird or trivial, but people are weird, so it's something that should differ by individual.

Let's look at a few examples, these are a mix of things from the comics and Avengers Alliance(because AA has a LOT of former villains as heroes):

Avalanche: In AA, he joined the Avengers because he felt the Brotherhood had gone off the deep end and had betrayed the cause they claimed to fight for. Then felt he had nowhere left to go.

Constrictor: In AA, he joined because he wanted to make the world a better place. He had more money than he knew what to do with from being a villain, and had no more reason to be a villain.

Destroyer: Yes, that massive self-animated walking armor from the first Thor movie. In AA, Loki and Amora enchant it to serve SHIELD instead of destroying things while rampaging.

Doctor Doom: He'll do whatever he think he has to in order to accomplish his goals. In AA, his over arching goal was to solve the Incursion problem and eventually he decides that helping SHIELD was the best method.

Elektra: Um... She's a hero approximately whenever she feels like it.

Enchantress: In AA, Thor's been hanging out with SHIELD and Amora misses him.... so she decided to join SHIELD in order to have more time with him...

Fixer: In AA, Fixer got bored of being a criminal. so he decided to try being a hero instead. Also he apparently thinks MODOK is an idiot, not stupid, just dull witted.

Juggernaut: He's had several reasons on various occasions. In AA, he simply decided he was tired of losing to heroes.

Kang: He saw the end of the universe, and saw that he had to help you in order to stop it.

Loki: well.... he does whatever he wants. Sometimes he wants to help heroes.

Magneto: classic case of an anti-villain. He has good motives, but bad ideas on how to achieve his goals. He simply chose to use better methods.

Moonstone: She's kinda amoral, but doesn't want to think of herself as evil. She wants to think that she's just another person and that many people would have done similar things. But that means she will also do good things if she thinks it will help her.

Omega Sentinel: Well, Karima Shapandar never wanted to be a villain. She got turned into a cyborg by Bastion, and that was the only reason for her being a villain at all.

Sabretooth: Him as a hero is usually because he's been forced to do so through some threat of death or something.

Sandman: He's the sort of guy who just doesn't really know what to do with himself. He was a small-time thug before he got powers and didn't really know what else to do. Eventually he simply decided he didn't want to be a villain.

Satana: she wanted a place to hide after other demons tried to kill her. She was like, "ok fine, I'll help you if I can live here for now."

Taskmaster: He works for whoever pays him best. But, in AA, he found he couldn't count on getting paid as a villain since the other villains often got taken out before they could pay him what they owed him. So he decided to be a hero... for the paycheck.