When I used to work in an office environment I used to respond to emails almost immediately. This was only because most of the emails I got were internal and if I didn't answer right away that person would through my door. Eventually I started closing the door so they would literally knock.

I work for myself now, and am solely responsible for sales, marketing and customer support. I'm on my email all the time, BUT I don't respond right away. Since I travel frequently (nine countries in the next month) and am in some wacky timezones, I've become really good at prioritizing emails and tasks. An urgent issue for a client takes precedent over a sales inquiry which itself takes precedent over social media or a new comment on my blog.

That said, I often will email back a quick note to people I know, saying hey, I got this, I'll get back to you in detail later on. Sales inquiries take a little more time as I like to do a bit of research, and therefore need the laptop or ipad instead of my phone, but even then I'll email back asking a couple of general questions to at least buy myself some time.

TLDR; I check it often, but only respond once or twice a day. At the end of the day, I'm always at inbox zero.