All browsers will leak a lot of data about you and that is a fact. Addons help eliminating many – if not most – of the privacy breaches, but you still have to verify what’s going on under the hood.
BrowserLeaks
BrowserLeaks is a site that can show many insights on what your browser is giving away. It runs tests for IP location, DNS detection, WebRTC leaks, JavaScript, Fonts and other technologies. It is clean and most importantly: very accurate. In testing, I found it to do a better detection job than most other similar sites.
Cover Your Tracks
Cover Your Tracks is a project provided by EFF Foundation. It tests your browser for fingerprints and gives a score and recommendations for improvements.
DeviceInfo
DeviceInfo goes far beyond basic IP info and it can detect so much info on you that it is scary: resolution, CPU, logged-in accounts (e.g. Google, Youtube) and much more.
Have I Been Pwned
Have I Been Pwned isn’t a test tool for your browser fingerprinting and leaks like those mentioned above, but one to check if your email address has been leaked in exposed databases. The biggest problem with those database leaks is that they contain the passwords associated to users accounts and once leaked, attackers will add them to their automated bruteforce bots and try to login all over the web. For this reason, reusing passwords is a very bad idea so you should use only strong passwords, unique for each site/service. And that is where the passwords managers come to rescue.
Other good leak test sites focusing on detecting VPN leaks: