Perhaps try to help them to resolve the issues and cope with the stress of being upset. They need to learn to use their words to work out problems, trade, take turns, and work out problems in a diplomatic way... like adults should (as we hope the government would more often... hee hee).
Sit with them and help them work out their little issue for the day. One of the boys wants the toy, then I try to help them barter the other child for a different toy or take turns, toss a coin, or no one gets it and they need to find something else to do. There should never be hitting.
When my boys fight, hit, hurt feelings, I encourage them to say sorry for hurting the other, give a hug, etc.
Kids are learning social skills that will pull them thoughout every situation in their lives. I hate it when my boys fight because I know they use those same reasoning skills when they're around other kids. I don't want my kids using fighting, hitting and name calling as a last resort to get what they want. I think they need to learn they are not always going to feel like they won after the battle. They should feel content with working things out.
Talk out sharing, finding more toys, using the toys in a different way, or putting the toy aside and finding something else to do. Help them think outside the box of reasoning to find resolutions. If they both want the same Power Ranger or Basketball, help them make up a new game where they both get to play with it. They can run the toy through a little obstacle or war scenario. Each time they get to a certain point they get to fight with the Power Ranger. Then they go onto the next little fighting scenario. They could play basketball and shoot from one spot with the special ball. Then when they go to the next spot they use a different ball. Or you can always resort to playing with it for five minutes then switching. Or playing with it for the morning, then switch in the afternoon.
Or help them work out different things like having a friend spend the night or going to the movies and choosing which movie they want. Use your imagination.