I babysit three cute boys, the oldest, 11, and twins who are 8.
I babysit them 9 months out of the year, around school, and then I'm off during the summer.
One of the twins, max, has a tendency to cry to get his way, on other instances we will be playing a game, such as cards, and if he finds himself losing, he quits and doesn't want to play anymore, the only time he ever wants to play a game is when he is winning or knows he will have the advantage. Sam, his twin brother, tends to take pity on him and allow him to get his way, and I'm only assuming that if he's showing this kind of behavior around me, his parents allow him to do this as well. (My action to this kind of behavior so far has been explaining that no one is going to want to play with him if he doesn't play fair, and see the game through to the end, as far as him crying to get his way, I have just watched and observed. He has however, learned that from me specifically I will not allow him to get his way.)
So I am curious if there is anyone who can give me advice on how to break this habit, I want these kids to grow up well adjusted, learning the right way to handle things. And since I will be a big part of their life during the school year, I'm wondering what I could do to influence them into better behavior, since I consider myself a persistent role model in their life.
Also, when these boys are fighting and being vulgar towards each other verbally or physically, timeout is beyond them and it is hard to enforce, so I am wondering if there are any effective measures I could take so that they will stop the bad behavior, and recognize that the behavior is bad but not to be repeated.
I have reported all of these instances to the parents, and their response was to either threaten to call their father, or separate them till they calm down.
But like I said, I want to know if there is more I could personally do without stepping on the parents toes.

Have you presented the parents with your concerns in the same manner you've presented them to us? It's the parents' choice how/when/where the children should be disciplined. I would not want "my" babysitter to take matters into her own hands. I would expect her to work with me.

It is not your choice what punishment should be used, and of course time out works for 8 year olds, if they know the parents will unhold it.

Well, I do know that the twins behvior, of one covering and giving into the other, is normal twin behavior. One is the dominant and one is the submissive twin. It sounds like max is the dominant. So the other boy does his best to make sure his brother is happy because he loves him. That is a good thing.

Other than that, talk to their parents. Let them know your concerns and ask what they would like for you to do about it.

Try team games, or games where everyone gets a chance to win, like setting up a mini assault course and the boys have to beat their best time.

Have rules for the games and get the boys to help draw up the rules, if their involved in the process their more likely to stick to it.

You can ask permission from the parents to set up a reward system, something very simple like a star chart, ask the parents for a list of small rewards the boys can have, each boy gets to pick something off the list if he reaches 5 stars...

Help the boys reach their star target, set them up for success by getting their input on what deserves a star and what does not.

Also if an row breaks out give the boy who's causing it a chance to say sorry and make up, give a way out.

A project for the summer might be an idea, planting a garden, or vegetables, get them excited about growing their own stuff, getting them to work together and help each other, but also giving each his own job and responsibility, this will help promote a feeling of pride and self confidence, the importance of follow through and team work, not to mention the childhood memories.

Their still very young and learning about good and bad behaviour, keep their routine and structure and be consistent in whatever you do.

You don't say what age you are, so that might hinder your authority over them, the parents expect you to keep order, their children entertained and of course safe, if a behaviour is out of your control it needs to be addressed by a parent straight away.