Major peer pressure starts around 8 years old. It is possible that she is asking for things that she feels she 'needs' to get along with her peers. Talk about this with her (talk to the teacher first, to see what is happening in class).
Is she crying when she is frustrated about other things, other then not being able to have what she wants? ie homework, school work, sharing, etc.
If that is also a problem she may be feeling more pressure at school (which you may not even see as a change simply because you don't see it). Speak to the teacher about this as well.
Overall, the best thing to do is model what you do when you are frustrated, both about not being able to have what you want and other frustrating experiences. I have even staged experiences like that so that I can model the behavior.
Don't give in to the crying. Calmly say something like, when you are done crying we can talk about why you are frustrated (give her the words for her emotion). You may need to repeat this to her more than once. I would also recommend, if the crying continues and it is disruptive (ie loud and distracting to the rest of the family) remove her from the room, explaining that we speak with words and when she is ready to use words you will discuss with her what the matter is. In this way she will hopefully learn that words are more effective than tears (this has worked with all my kids) after she comes to you when she is done crying help her express herself by giving her the appropriate emotion words. Show her lots of love and help to problem solve (WITHOUT giving in to what she wants).