Risk 1: Search data and metadata
If you visit Google's Web History page, you can see every single Google search you've run, while signed into your Google account, for years. And it's not limited to text searches -- you can also see your history of Google image searches, Google video searches, Google Maps searches and so on. This data is stored by default; users must activate Web History to access it.
Google uses this information for a number of benign purposes, such as fine-tuning its search algorithms and determining wider patterns in Web searches for its Google Trends page. But however useful it is to the company, it's probably a safe bet that you don't want anyone to see every search you've ever done.
The simplest thing you can do to prevent the accumulation of search data is to make sure you're logged out of your Google account before searching. If you're logged in, your e-mail address will show up in the upper right-hand corner of Google's home page, search results pages or any Google Web page you're on.
Also, turn off Google's Web History. From the upper-right corner of Google's home page, choose Settings --> Google Account settings, click "Edit" next to "My Products" in the left-middle of the page, and click "Remove Web History permanently." (If you don't see this option, it means you never initially activated Web History.)
This will unsubscribe you from Google's Web History service and erase all the specific data linking your account to your searches from Google's servers. Google will still keep data associating your searches with your IP address for nine months and with other nonpersonal information for 18 months, but this data is not specifically linked to your identity.
However, the Web History service can be of value to individual users, not just to Google. A searchable history of every Web search you've ever run could be a powerful tool for your own use. If you're comfortable with your search data being available in Web History but want to prune a few "incriminating" searches from the list, choose Web History under My Products from your Accounts page and click "Remove Items" in the left-hand menu. This will place a checkbox next to each query in your history; select the ones you want to chuck into the Memory Hole and click "Remove," and they'll be deleted.
You can also click the "Clear entire Web history" link at the bottom of the page to delete your past searches all at once, or "pause" Web History for a while, if you know some of your upcoming searches might be difficult to explain or reveal too much personal information. To put Web History on hold, just click the "Pause" link in the left menu, then click "Resume" to have Web History begin saving your searches again.
Logging out of Google prevents the direct association of searches with you, but not the searches' association with your IP address and other information such as the operating system and browser used, time and date of the search, and the ID of the cookie saved to your computer for that search. (Google's Privacy FAQ shows a sample log entry.) A determined attacker could conceivably work backward from Google's server logs to discover your identity.
To prevent this, anonymize your Web use by using tools like Tor, Anonymizer or the PhZilla Firefox extension. These tools funnel your Web use through one or more proxies, bouncing from city to city around the world, so your searches cannot be traced directly back to your computer. Be warned, though: Internet surfing is significantly slower when it takes place behind a proxy server.