Let's say that you are the webmaster of a fan run science fiction convention, say Star Base Indy, and someone tells you "Feature xyz doesn't work on mobile" – what do you do? You might dig up a phone but you could also try out Responsinator!
Responsinator is a tool which lets you put in your own url and then view it as if it was a mobile site. Try it here.
Here's the description from the authors:
"Responsinator helps website makers quickly get an indication of how their responsive site will look on the most popular devices. It does not precisely replicate how it will look, for accurate testing always test on the real devices."
Responsinator isn't perfect but it seems like a very cool, very easy way to get a feel for whether or not your site works on mobile (at least in terms of rendering / display). Strongly Recommended.
Postscript: There is even a bookmarklet that you can put in your browser toolbar to test whatever site you happen to be working on