Some companies will take advantage of it and pay you lower, some won't. My current employer offered me more than what I was asking for due to their internal equity program.
What state are you located in? In many states, it's illegal for a potential employer to ask candidates about their salary history. If they do ask, turn it around on them and reply with something like, "I don't want my current salary to be a factor in determining my future salary. Would you mind sharing the salary range for the role?"
I work in recruiting, BTW.