This page Shows you What EVERY Website you Visit Sees about YOU and your Computer. If you are running your computer through a proxy server websites would see the proxy servers information and you would be completely hidden.
In addition to the above information your IP address comprimises your computer privacy and security in the following ways:
Every website you visit can see every page you view and for how long.
Certain web browsers (chrome) store every single search engine search you make as well as every page you visit. This is because Chrome is made and owned by the search engine giant so by spying on every move you make "helps them to tailor results to your specific preferences for a better search experience"(bs talk for market to you). Read Chromes privacy issues.
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