I wouldn't go into the interview with the intention of crying, but some stories and explanations can catch you off guard and may elicit an emotional response. This is not a bad thing, especially if you have a good rapport with your interviewer. It's most important that you are able to convey your feelings and thoughts coherently before you feel that knot in your throat, otherwise the interviewer might not be able to empathize with you.
If you begin to get overwhelmed, you may always pause, take a deep breath and collect yourself before speaking again. That shows maturity and the interviewer should respect you for it.