Most questions that you get asked are technical in nature and specific to the job they are hiring for. So it is not uncommon to have people answer questions in a technical and pretty sterile way. And most people don't add much in the way of conversation, which can lead to awkward silence or the uncomfortable feeling for everyone in the room.
Selling yourself means answering more than the question on the table, answer it with examples to show proof you know it not just read about it. People have to feel like you did more then stayed at a Holiday Inn Express last night, they need to feel like you really know and can demonstrate it. So examples are good, past experience good and bad is relevant and helps. Asking questions during the interview that are detailed and show you have studied the team, individual or at least the company goes a long way. Also, asking questions during the interview instead of waiting until prompted can many times throws the interviewer off the question/answer method and turns it into a conversation instead.
Treat the interview like you would a date and that alone goes a lot to selling yourself. Turning the interview into a conversation where the interviewer comes out knowing you are competent but you can also communicate. Learning to do this takes a little practice, but it is just common social skills mixed with asking questions so you can open conversation paths. Think about any date you have witnessed or been on where it was awkward and there wasn't any give and take during the conversation, it never ends well, same with an interview.
You won't be able to do this with everyone, there are people that are so nervous themselves or such complete asses that they won't budge, so just hammer through those best you can and move on to the next interviewer or company.
edit: BTW humor goes a long way many times. Breaking tension by recognizing it and saying something can sometimes be the fastest way to get people to let their guard down.