They can only keep that sort of deep data for so long due to storage requirements - I think in the uk at present it is 30 days. If your chosen search provider keeps a handy list of your searches forever associated with your account though, it makes life much easier for agencies to access it at any point in the future and replay your life. For someone with mail at gmail and web history on, that anyone would have that much data stored on you is a scary prospect.

There are other much better reasons not to prefer google as your search company though, foremost among them that they sell advertising and are no longer in the growth stage but the monopoly stage of the corporate lifecycle, so their incentives are not really aligned with free search customers. Their dominance of web search is starting to seriously distort the web.

Donttrack.us Dontbubble.us

They log queries but in an aggregated way not tied to specific users or sessions (not even pseudonymous user IDs or IP hashes): https://duckduckgo.com/privacy#s3