Google have provided a tool which checks to see if a site renders clearly in a mobile browser. The tool looks like it is setup at 320px and if your site works at this you’ll get a “mobile-friendly” tag in your organic search listings.
Here’s the link to check your sites: https://www.google.com/webmasters/tools/mobile-friendly/
Some other good sites for checking across different screen sizes/browsers are:
http://validator.w3.org/mobile/ – Validates markup, I always have a lot of time for Tim Berners Lee
http://quirktools.com/screenfly/ – This is useful for checking resolutions across mobiles and tablets.
Even if you aren’t expecting SEO traffic it’s still worth checking these for mobile landers as you might notice some bugs or something you could have missed previously.
It’s a shame Google haven’t had time to get their own sites compliant 🙂