Clearing your browser history can be deemed 'obstruction of justice' in the U.S
cbc.ca
cbc.ca
Clearing your browser history, just by itself, isn't obstruction. Clearing your browser history and cache, when some of the information present there is evidence relevant to a criminal prosecution in which you are a suspect or a witness, can be, especially if you do it to try to cover up your involvement, and that shouldn't be surprising to anyone.
except, y'know, when it's material evidence relevant to an ongoing investigation being destroyed to cover up a crime