You may find the need to log in to more than one Salesforce environment at time on a single computer (for example, your production org at work to do your job and a developer edition org to perform testing).  Not to worry, there are a few solutions for this:

1. In Lightning Experience, you can add additional logins and then switch between users.
2. Navigating to the login page will allow you to switch between multiple active sessions.
3. You can use create Chrome profiles and establish a unique session for each profile.  I highly recommend this approach (even if you are using Lightning Experience), as each Chrome profile can have a separate icon and function (which removes the “wait, what org this again” syndrome).
4. You can install many browsers (Chrome, Firefox, IE, Safari, etc.) and use each browser to maintain a separate session.

Notes:

• Session management (#1 and #2 above) is managed separately for production and sandbox environments (you cannot add a sandbox session to a production session).
• You can only maintain one session per pod per browser (in this example, cleugb@gmail.com and cleugc@gmail.com are both hosted on NA50, so I would need separate browsers if I wanted to connect to both at the same time).