Great question! It is very important in an interview to be yourself and not too "robotic." However, being professional and focused is also key. So setting the tone in an interview does make a big difference. My recommendation is to be very professional from the start and let the interview take its course. You will get an idea for the person who is interviewing you and if they crack some jokes feel free to laugh and if you think it is appropriate you can tell a funny story that applies to what you are talking about. For example, when you prepare for your interview think about answers to questions such as :
1) Tell me about a challenge that you had at a recent job and how did you over come it?
2) Tell me about a recent accomplishment and how did you set out to achieve it?
3) What is your biggest strength and what is your biggest weakness?
These types of questions come up a lot in interviews and give you a chance to show the interviewer who you are by telling a personal story or experience.
Never make fun of the person interviewing you, do not tell stories that make others look bad, and if in doubt do not make a joke if you are unsure of the way it may be perceived. Be polite and try to be as honest as possible. It's normal to be nervous during an interview so if you prepare a lot ahead of time this will help when the time comes. Good luck!