Tor Browser provides anonymity to users by anonymizing user traffic through a distributed network of servers called nodes; however, it does not provide complete anonymity.
German intelligence services recently identified a Tor user through 'timing analysis' in which authorities monitor Tor exit nodes and trace anonymous connections back to the end user.
The more nodes a country has, the more of them can be state-monitored, increasing the likelihood of catching criminals.
The Tor Project includes safety tips on their support page, but anonymity online primarily depends on the actions of the user rather than the technical capabilities of the browser.
If you're using anonymous browsing simply to avoid intrusive contextual ads or for harmless purposes, private browsing mode in any regular browser should suffice.
Kaspersky's home security solutions include Private Browsing that detects attempts to collect data and logs them in a report without blocking them.
Kaspersky VPN Secure Connection offers Double VPN that allows you to create a chain of two VPN servers in different parts of the world that provides an additional layer of security and anonymity.
It is essential to remember that traffic encryption methods are not intended for illegal activities and only conceal personal information from data-gathering sites.