Oh Tindytim, they need your IP address to better tie their on-page ads to your last 18 months of searches. By knowing that 18-months ago you searched for summer vacation destinations, they can provide better ads for your latest query on cold remedies. Google is a lot smarter than we, the simple computer users, so we have to trust they know better than we do.
To be more serious, I also don't understand why they need IPs. They process millions of queries and ads a second, so I can't imagine any single user could do anything to scew their algorithms in any meaningful way. I mean sure, they need to make sure that someone isn't scamming their Ads by sending thousands of clicks a second to a competitors link, but why they need to maintain that information for more than a day is unknown to me.