If you think you can get away with not telling them then don't tell them. The caveat is that if you refuse to play along then it may end the interview process right then and there. In that case, if you would have been willing to entertain an offer of "whatever you were getting paid at your last job plus a small delta" then you your decision not to play along was in error.
Unless you were drastically underpaid at your last job relative to the one you're interviewing for, the new job's offer will be whatever you were getting paid at your last job plus some amount that's 1. big enough to not be trivial, but 2. not much bigger than that. So maybe $5k/yr. That will be the starting point of any post-offer negotiations. Your leverage is low, though, because you already told them what you were making before.
Another tactic is to answer the question, but ask them for similar information in exchange. For instance, "What's the average compensation for someone with my experience in this position that I'm applying for?" If they won't answer, the you can credibly say, "I'm not sure I'm comfortable divulging my compensation history if you're not willing to do the same. Does that seem fair?"