I have that same kid it seems, but she's now 8 and going into 3rd grade. I've had this issue since Pre-K with her. They almost didn't pass her to Kindergarten because they said she was too immature to handle it because of the crying. First and foremost, really think back and try and determine if she is a sensitive personality. I had never given that any thought, but in reality, my daughter has been sensitive her whole life. Step one is accepting that she is a sensitive personality and probably always will be. So our job is to teach our daughters how to cope in the situations when they want to cry.
So, starting with Kindergarten, at the beginning of the year, I always tell her teachers that she is a more sensitive personality. I don't expect special treatment for her, but most teachers have dealt with sensitive kids and know how to work with them. Work with your daughter's teacher from day one and try to handle situations as the teacher does so you can give her some consistency in the kind of behavior expected.
On the other side, we've really worked with her on controlling her emotions. We say, Samantha, take a deep breath. Calm down or we can't help you. We stopped being all "oh, what's wrong, oh poor thing" because she's crying (unless she's hurt physically of course). We have had to pretty much put our foot down and tell her "use your words." It has worked. In fact she did great in Kindergarten because she was constantly being kept busy and told, "Use your words". In first grade, she got weepy in the beginning of the year, probably due to the adjustment of a full day, but really no problems with excessive crying. Last year was tough though as some girls got that whole "mean girl" thing going.
Unfortunately, this kind of personality tends to lead to my daughter tattling (she replaced crying with tattling) and being the target of bullies because bullies love to make others cry and my daughter obliges. I actually sent her to the school counselor this past year because the crying was rearing it's ugly head again. It really helped her to hear coping techniques from someone else. It's true, your daughter might get called a cry baby - mine did.
My last words of advice would be to try and get her into something that increases her self esteem so that she feels she can stand up to others and care less about what other think. I didn't realize it back in Kindergarten, but some of the crying and sensitivity has to do with lack of confidence and caring too much about what others think. My daughter has a hard time standing up for herself (she thinks it's being mean). Once we were able to teach her the difference between standing up for herself and being mean, it made a difference. She also has a hard time walking away from situations. We are trying to teach her to say things like, "If you're going to not play nice, I'm going to play elsewhere" instead of taking it personally and crying. We've had some success.
Good luck. It's not an easy thing.