This depends entirely on how you use email.
I do almost zero personal communication via email. It's all notifications, receipts, etc. Thus I check it maybe 4 or 5 times a week.
The frequency I would check my email would vary if I did personal conversations, or business conversations, or support, or etc.
On top of that, with GMail (or Google's Inbox), you can set up all sorts of filters and searches. My phone notifies me of new emails from my wife, whom I know doesn't abuse email, but new emails from my mom whom is likely to be forwarding me something...mom-ish...get read when I do my several-times-a-week look over my inbox.
That would be a cool feature for phone calls. Depending on situation (or mood), switch between happy hours where everyone gets through, serious caller only mode for business hours, and emergency mode for anything social or serious.
How frequently do you think you *should* check email? You can also say how frequently you do in comments.
Personally I'm sold on thinking you should check it around once a day, not necessarily without fail. That increases focus on both email and non-email, and minimises getting sucked into distractions. But some people I know disagree. Some believe in getting notifications whenever a new email comes in.
For anyone who'd like to check email less often and uses GMail, I recommend using http://inboxpause.com/ and this full screen compose link: https://mail.google.com/mail/u/0/?ui=2&view=cm&fs=1&tf=1&shva=1
Edited to add: I'd recommend everyone at least try checking only once a day, at least for a few days, to see if you find it more productive and/or relaxing. That'd be a big enough win to make experimenting worthwhile.