Multiple login in one browser

Firefox

In Firefox, you can have separate sessions with the Multifox extension. Unfortunately, it requires sessions be in separate windows instead of separate tabs.

The same developer is working on a new extension AllAccounts which is still in beta, but does support multiple sessions in the same window.

Chrome

For Chrome, there is an extension called MultiLogin, which gives support for different sessions in each tab. Note that it is only free for personal use, so if you are using it at work, you may have to email the developer to inquire about a commercial license.

Internet Explorer

As far as I know, there is no extension for Internet Explorer that allows for multiple sessions in the same window. But for IE10, to get a new session in a new window, press alt to open the menu bar, then click File->New session.

Testing

To test multiple sessions, you can try using the very handy IE browser session test page. You can set the background color of the page, then open it again in a new session and you should be able to set a different background. It also displays what sessions are being stored in the browser's sessionStorage and localStorage.

These are the results from my testing with Firefox 36, Chrome 41 and IE 10:

• Multifox v3.1.0: Each session has separate sessionStorage and localStorage
• AllAccounts v2.1alpha3: Each session has separate sessionStorage and localStorage
• MultiLogin v0.1620: Each session has separate sessionStorage but shares localStorage
• IE 10: Each session has separate sessionStorage and localStorage

Set your web browser to block cookies for the site. It will prevent auto-login when the tab closes but, for many sites, that won't prevent you from logging in.

Chrome Browser:

You can use MultiLogin as suggested in other answer or to create multiple login screens in different tabs within same Chrome window you can use other extension, it's really good and I'm using it: SessionBox