I don't generally do anything "incriminating" that would need to stay out of my browser history, and even if I did, clearing your local browser history isn't going to mean much: If it's truly criminal stuff you're talking about, all the websites you use are likely subpoena-able anyway and they'll get your "history" one way or another.

For mildly "incriminating" stuff that isn't illegal, just use an Incognito window. :-)