The above answers are great for those who like to stick with a single browser, or have limited desktop "workspace" (eg. single monitor less than 21" at a low res).
There is actually an even more interesting solution I've recently discovered: https://blisk.io/
I will refrain from using the (sort of) "affiliate link" for any personal gain (There is a "token based system" that you can earn credits to get things like free "team cloud space" & "premium features" to use with it), but Blisk is actually pretty snazzy.
This Chromium-based "browser built for development" provides a multitude of ways to demo the page in various devices with a vertical "pane" on the LEFT side, much like you see Chrome Developer Tools default to the right vertical column.
It's work a look. Though there are some limits to its "freemium extended functionality", it still works very well to "preview" both the PC and Mobile versions of your pages / sites in a side-by-side comparison. The paid features seem pretty rad too if you work in remote teams (though I personally think it need a better "test drive" program before hooking people on the monthly cost).
Full disclosure: there is an EXTREMELY annoying "time limit" per day on the mobile preview part (toggles open/closed from the icon to the right of the address bar - change the "device preview" from the tiny link-to-the-menu in the top right corner "Show device list").
I've found a few really nifty tricks with Browser Extensions like the 2 different "User-Agent Switcher"'s from Chrome/Firefox that go a bit further by letting you toggle between browser user-agent strings of various Operating Systems AND the browsers for them.
I prefer the "esolutions.se" flavor because of how easy it is to add custom user-agent strings to the list for as many customizations as you could ever want (runs offline also, which can be handy in certain cases):
Anyway, that's my 2 cents. :P