The first major browser to take the throne from the old Internet Explorer was the famous Mozilla Firefox, which is still very popular and well-liked for being from a small, independent company that just wants a free and untampered internet. It is very fast and with a multitude of free plugins.
On the other hand, after a while the Google Chrome, another classic browser and the current leading browser, which was imposed on Firefox, not because it is better, but rather because of the power that Google has; a huge company that, similar to Microsoft, tries to impose its power, against a small company like Mozilla.
Another very popular and well-known browser is Opera, or Safarion Apple systems.