Google is now allowing users to download a copy of their search history. Quietly introduced in January and only recently picked up on, it's relatively easy to snag a copy of your search history. First, you'll need a Google account. From there, pop over to your Account History page, click the cog in the top right of the screen and select Download.
Once you agree to Google's brief albeit important notification, you can click Create Archive at which time the search giant will compile your search history into a JSON file sorted chronologically by quarter. Once complete, you'll receive an e-mail with a link to your search history in Google Drive that can be downloaded as a ZIP file.
The notification that you must agree to is rather humorous as Google suggests it's not the "usual yada yada" and that you should read it carefully. Basically, Google is warning you not to download on a public computer as the archive contains sensitive information. What's more, Google urges users to enable 2-factor authentication (an all-around good idea anyway).
Note that search history will only be reported once you've enabled "Turn Web History on" in the Account History page.
As for why you'd want to download your search history, that's up to you. Outside of the potential for some embarrassment, this is really just Google's way of complying with the whole "you own your data" notion as other companies like Facebook have adopted similar "download your history" options in years past.
Images via SearchEngineLand, Unofficial Google blog