Mailbox for Mac
Our sister site, The Sweet Setup, recently picked Mailbox as their favorite third-party email app for the Mac. Jason Snell points out that Mac users have a love-hate relationship with Apple Mail. While it's built in to every Mac, it's gone through periods of major instability (particularly with Gmail IMAP). After reading the article, I downloaded it to give it a trial run. While it only works with iCloud and Gmail, it's a very powerful app.
One of my favorite features is that I can "snooze" particular emails until I move to the desktop app or vice-versa. This is handy when I receive an e-mail that requires me to do something that can only be done on a Mac.
It's still in beta, but I've found it to be fairly stable. You can download it for free.