In addition to the many things that have been already mentioned, one of the most important advantages of a debugger over printf is that using printf statements assumes that you know in which function the bug resides. In many cases you don't, so you have to make a few guesses and add print statements to many other functions in order to localise it. The bug may be in framework code or somewhere far removed from where you think it is. In a debugger it is far easier to set breakpoints to examine the state in different areas of the code and at different points in time.
Also, a decent debugger will let you do printf-style debugging by attaching conditions and actions to breakpoints, so that you still retain the benefits of printf debugging, but without modifying the code.
