[UPDATE 2/22/2012] It is important to note that disabling Web History in your Google account will not prevent Google from gathering and storing this information and using it for internal purposes. More information at the end of this post.
Here’s how you can do that:
1. Sign into your Google account.
2. Go to https://www.google.com/history
3. Click “remove all Web History.”
4. Click “ok.”
Note that removing your Web History also pauses it. Web History will remain off until you enable it again.
[UPDATE 2/22/2012]: Note that disabling Web History in your Google account will not prevent Google from gathering and storing this information and using it for internal purposes. It also does not change the fact that any information gathered and stored by Google could be sought by law enforcement.
With Web History enabled, Google will keep these records indefinitely; with it disabled, they will be partially anonymized after 18 months, and certain kinds of uses, including sending you customized search results, will be prevented. If you want to do more to reduce the records Google keeps, the advice in EFF’s Six Tips to Protect Your Search Privacy white paper remains relevant.
If you have several Google accounts, you will need to do this for each of them.