It is more important than ever that websites are reponsive to both the type of browser and the device which they are viewed in.
Here is good site to check your website across various devices:
http://quirktools.com/screenfly (my new favourite!)
Here is an instant checker (although I am slightly weary of this one as the results don t always seem to be true):
And here is the way that Google checks if you site is mobile friendly (Good for SEO)
And across different browsers: