You may or may not know, but Google is changing the way it ranks websites from the 21st April.
The new algorithm takes into account if your site complies to their requirements for mobile friendly websites. Note that this is to Googles requirements.
If your site does not comply they say that you will receive a drop in search rankings over sites that do comply to their requirements.
Many sites do work well on mobiles, but for various reasons they do not comply to Googles requirements . They will therefore be placed lower down the search results.
Google do offer a simple check here so you can see for yourself if your site is acceptable to them.
Have a look at your site now and get it fixed before it is too late.
With regards to Amazon and eBay, all is good for the listings, but having looked at a random sample of 100 ebay stores, they have all failed the test ! That includes those with or without 'mobile friendly' templates.
[Last edited: 20 Mar 2015]
E-commerce , love it or hate it, that's why we are here
There's also the new Mobile Usability report in Google Webmaster Tools. GWT is a great resource and provides a lot of information on how Google views your site, definitely worth registering there.
By the way, the new criteria only affect rankings for mobile searches - desktop is unaffected.
I received the dreaded "Fix mobile usability issues" message for Web Retailer yesterday (I was expecting it). Mobile usage on WR isn't as high as shopping sites (it's 19% phones, 7% tablets) and of those about half arrive from Google search and half by other means. But it's still significant and needs fixing.
Also shouldn't ignore that the changes Google suggests should genuinely improve mobile usability so it's not just a case of jumping through hoops to please Google.