I don't have a smart phone
I have recently become convinced that email belongs in the web (for a PC user at least). Like Promit said, having a tab open and receiving desktop popup notification is practical enough for most cases. GMail is the standard, but I just don't feel comfortable with google trying to know everything about me - they already know what I search for and what I watch on youtube. As mentioned earlier, it probably wouldn't make much practical difference if they can read my emails; I already know extra sensitive and private things don't belong in emails, but I can't help but want to stay away from google whenever possible.
Outlook.com (not outlook the application) is an alternative. Microsoft basically says they care about our privacy more than google, but outlook.com works with external email accounts (like the ones on my domain) in a suboptimal way if my understanding is correct: you'll have to set your accounts to forward all received emails to your outlook inbox instead of outlook checking for messages itself. Also, I've noticed outlook.com failing to display emails correctly (or at all) on a few occasions.
I'm still researching for the best solution, although I'm starting to feel I should just pick something and go with it as long as it works and stop making a big deal out of the small inconveniences.