I've tried Spark, Inbox, and Outlook. I'm an inbox zero adherent. The clear and unequivocal successor is Polymail (in alpha)--at least for now. None of the others do snooze as well as Mailbox did. I expect Polymail will fill that spot. Sad to see no one's mentioned it yet, as they're getting a lot of buzz. They'll be releasing an iOS app in early 2016 as well.
chew85 below recommended Polymail, which looks like it will hopefully become the best solution to replace Mailbox.
In the meantime, thanks for the tip about turning off bundling as I've switched to Inbox for the interim.
I just ran into this app that looks promising, polymail, while digging through the dropbox forum of people complaining about the shutdown. Looks like it will actually be a mailbox replacement if all pans out. Alpha seems to have just come out for mac, and iOS app soon according to the dev's twitter. I'm glad to finally have hope again.
I could never stand Inbox, was figuring I'd have to get used to Spark which seemed like the next best thing.
Polymail is winning the Mailbox-replacement war. I love it and many think it's the clear successor. It won Product Hunt's Mac App of the Year. The two hurdles it currently faces:
They're planning on releasing an iOS app sometime in early 2016. No email client comes close to replicating Mailbox's most beloved features. Inbox, Outlook, and Spark only partially match some of UX. I've found Airmail disappointing.
As a previous Mailbox user I'm not a fan of Spark's design at all. Those buttons are one of the main reasons I don't already use Inbox. Also really hate the sectioning/pinned email stuff.
Not sure what I will do about iOS, but I am currently keeping an eye on Polymail for the Mac.
Another poster suggested PolyMail which is in beta and has all of those except an iOS version which is in the works. I would also add lists as an essential for me though I don't know if you can automatically send certain email to a list yet, granted I haven't looked too deeply into that functionality yet.