Not many '0' queries--that term's ranking is about #2000 in this data set.
We're planning on removing IP addresses from our logs after a year, but keeping them in some form indefinitely, as per our privacy policy: http://duckduckgo.com/privacy.html. However, we're very open to suggestions on this front. Right now, as it has been less than a year since we went public, we have everything.
We don't use cookies at the moment because simply there hasn't been a pressing need to use them. We may start using them, however, to store things like language/region preferences.
How many days do you store logs? Why don't you use cookies? How many people searched for "0"?