Understanding Mailbox
An alternative email app called Mailbox was released around 2 weeks ago with a lot of positive words from the press and many negative words from those with a reservation.

The idea is simple, clear your inbox. And keep it that way.
This is something I've actively tried to do since discovering the purpose behind GMail's archive functionality. It helps to keep your inbox clear, but if I'm honest it's really just helped me to keep it tidy. I've had emails sit in my inbox for over a year and never actioned them to the point that they get archived because I know I will never get around to doing anything with it.
For me, Mailbox will hopefully change that. Not only can you archive and delete emails, you can move them to one of 3 dedicated folders; To Buy, To Watch and To Read. This neatly organizes emails that still need to be actioned and keeps your inbox clean.
Later
The killer feature though, is later. Later allows you to archive an email, until later. You choose when and the email will return to your inbox. This has been useful for me as I keep receipts in my inbox until the item arrives, but now I just set the email to re-appear on the day it's supposed to be delivered. And if the item is delivered early, I can always go into the later list and disable the reminder.
I didn't really get Mailbox at first, but after a week, it made total sense. I had already moved the Mail app from the homescreen to a a specific folder for unused stock Apple apps with the view that it would probably be coming back soon. Soon after moving it, I turned email syncing off and within 24 hours, I hadn't looked back.
Download it, try it, love it!
I cannot recommend the app enough, just know that if you download it and once you have access, it can take a little bit of time to get used to. When it comes to later, you have to put a lot of trust into the app and when they did go down for a few hours a week after launch, it was tough going! Luckily, GMail is web based and there is the stock Mail app to get you through any extended downtime.
Old habbits die hard
I filled a feature request and got something back from the Mailbox team. I guess they must be getting a lot of emails about the ability to use your own labels & stars. I have a lot of filters for applying labels automatically to emails from, say Apple (iTunes/hardware purchases) but there's no visibility that they've been applied. Funnily enough, I don't recall any visiblity in the Mail app either, but knowing that the Mailbox app is using a combination of the archive and labels, I still wanted some of the control over this.
It's another feature you have to put your trust into and to be honest, GMail itself does an excellent job at applying labels. If I want to continue to categorise emails into 'folders', then I just need to make sure my filters are as robust as possible. In the long term, this won't be a problem when dealing with the inbox, but loosing the ability will really be noticed when looking for specific emails.
BeUnequaled Magazine
One thing that concerns me about their move away from the 30-pin connector is that there's likely to be less strnegth when your device is docked. The 30-pin, while big, took the weight comfortably. The iPhone 5 may be one of the lightest ones yet and I'm sure these considerations will have been taken into account, but how will the device sit cradled loosley on a Lightning connection?