I also cry easily. It can be really annoying to cry at a commercial when I know I am just being manipulated. Hate those Hallmark Hall of Fame specials!
First, never buy into that claptrap about “you are too sensitive.” Turn it around: perhaps others who are making you cry are insensitive toads!
In the thread kevbo pointed out there were good answers (including his). gailcalled mentioned that women cry when they are angry. I have found this is true for me and for other women I have talked to. It is not true for men though so it puts women at a disadvantage in a workplace situation.
There is one other idea I might offer I did not see mentioned above or in that earlier thread that has worked for me. I once asked a singer who performed a lot of wonderful, but very sad songs how she got through them without crying. She said, “We sang them a thousand times while crying first.”
I have used that since. If I am going to talk to a boss at work and it is an emotionally explosive situation that I think might lead to tears, I practice what I am going to say over and over again in a mirror out loud until I can say it without any voice wobble or tears. Then I imagine the worst possible thing (in terms of triggering tears) the other person could say and practice hearing that and making my answer.