You don't necessarily have to turn it into a positive (like 'I care too much' or 'I'm too hard working'), but you should not let it leave a sour taste in the interviewers mouth. For instance, you shouldn't say something like 'I often leave things unfinished'.
My tactic is to use a real weakness, and explain what I'm doing to work on it. In my case, public speaking--I have a few anecdotes of disastrous speaking incidents, and emphasize what I have been doing to get over my fear and to become a better speaker. You could say 'I have some difficulty with organization, but have been working on a system that allows me to make sure I complete all my work in a timely manner'.