[...] What do you think of it? If you haven't done it yourself, do you know of any examples?
I think responsive is good. I want my websites not only to be "mobile-friendly", but also look good in different screen resolutions (for laptops and desktops).
There are many responsive frameworks out there. The most popular ones are
Bootstrap and
Foundation. My issue with frameworks is code bloating. And there are so many styles to override.

This takes so much effort compared to when I make my own layouts responsive. So I just do the latter.
You can also make your layouts fluid. Then, they will seem "responsive" even when they aren't.
Do you think it is worth adding to your sites?
Yes. I try to make all my websites responsive.

I don't have shrines yet, but I'm planning to create one soon. It would be interesting to see how I plan to incorporate responsiveness to shrine layouts.
Do you think your sites are viewed more on a computer or on smart phones/tablets now-a-days?
Some of my websites are viewed more on laptops/desktops instead of mobile browsers, but there are some which are viewed more on mobile browsers and tablets. So many people are using handheld devices to browse websites now, and I never know who's going to visit my websites. And like what @Camy said, there is a greater number of people who have phones instead laptops/desktops. I want to keep my visitors, so I'm playing it safe.
