I'm stuck with Google Mail, but I too am moving away slowly from Google. I hate how Google makes it difficult to have more than one account. Although this is mostly because my primary account is banned from YouTube (without explanation), and also from Google Play/Checkout/Wallet (failed debit card transaction??), and also from Google Checkout for Merchants (without explanation).
I hate being unable to buy Android apps :(
Edit: I just bought an email account from Namecheap.