Google just launched a tool that allows anyone to test his website and learn if it's optimized for mobile phones, tablets and desktops.
You can test your own website here. By the way, here are the results for our website:
Don't believe everything they say
It's important to know that, just like any other automatic tool, it only gives you an idea of how well your site performs. The tool isn't perfect and sometimes, gives some pretty weird recommendations. For example, if you test www.google.com, the tool will recommend that Google needs to optimize its photos and prioritize visible content. Also, when testing their own test tool, they don't get a perfect score either:
So don't take everything they tell you as the whole story, but it can still give you a good idea on what aspect of your website needs to be worked on and what to talk about with your Web developper.
UPDATE: It looks like Google made some changes after getting lots of comments about the performance of their own website. Here's their test tool's new score this morning: