Mozilla Firefox is a powerful opensource browser for your desktop or laptop. It is highly customizable and light on system resources. Their Extensions System is a great way to add new features and functionality and with it FireFox Sync, you can have your browsing history, stored passwords and extensions synced to all of your devices.
Google Chrome is an opensource browser that makes a great alternative to Internet Explorer. Developed for speed, you will be surprised just how fast your favorite web pages and web applications run when using this browser. You can sign-in using your Gmail account in order to sync all of your settings, extensions and history between your devices.