That's a bit of a short question Mark, an "?" are you a spambot?
A mentor spam bot
I've used <button> several times. I've also used <input> as well. I did find a problem with <button> in that it creating a different action for the button whilst pressed, it somewhat shifted the button a little, which in many cases was undesired. I did manage to fix this somehow by removing the margins and paddings, but was still a little puzzling at the time.
Personally I don't think it's a big deal in using button or input. I did happen to use <button> for buttons outside the form element also. It does look much better, however <a href="#" class="button">Button</a> in many cases would do exactly the same thing, so in many cases I use an a tag.