Looking at the new Gmail app in Android 5, they’ve replaced the default archive option with delete (like swiping right). Good Google!
ooh, really? Nice! Hope that happens in the iOS app too.
I’ve been using it for my personal email. My work email is on Google Apps and devoid of Inbox for now. But I’ve already established that Inbox won’t work for my work email.
As @sil said in episode 30, there are some people who love to label their mail to the brink of insanity… that’s me in my work persona.
I’m starting to love Inbox for my personal mail. It’s simple and clear and is making managing that mail so much easier - basically I just leave it to pile up and I don’t even care!
Interestingly, Inbox feels to me to be very much more than just an experiment… it’s almost like Google showing me what’s possible with the GMail platform. Right now, the APIs around GMail would allow me to create this kind of interface. If I don’t like Inbox, I could build my own UI and other functionality.
Google’s challenge: “Hey GMail users, look what can be done! Think you can do better?”
A couple of days ago I got the chance to use it - eventually. And I really like it, it’s neat! 
I rarely use gmail though, but it nicely combines all that social, payment and whatever stuff, even calendar. =)
I really wanted to like Inbox (I love the bundling and sweeping functionality) but I gave up on it because of some subtle but very annoying incompatibilities between Inbox and Gmail. The main one being that while pinning and starring might appear to be very similar concepts their implementation and functionality are completely different. Note that pinned emails cannot be identified in Gmail and you cannot star emails in Inbox. So if you’re using stars or pins I find it frustrating to use both apps in parallel, as @sil suggested doing on the show (Inbox on the phone and Gmail on the desktop).
The more I’ve used Inbox the more I’ve realized that it was never designed to be used in conjunction with Gmail. It’s actually quite weird to me why they made Inbox almost entierly compatible with Gmail, but not fully compatible. This is confusing and a source of frustration for adopters coming from Gmail. You are essentially forced to jump ship completely from Gmail to Inbox, which I don’t think many people are going to be willing to do, and so I don’t think Inbox will gain enough traction to survive for long.
The other issue that I found destructive to my workflow is the handling of labels in Inbox.
I wrote down some details on these issues over at reddit: https://www.reddit.com/r/GMail/comments/2ofxh3/why_i_am_abandoning_inbox_by_gmail/
To me it feels like Google don’t know who their audience is here. On the one hand Google has said that Inbox is designed for power users (who get a lot of email), on the other hand, the implementation seems directed to “new” users (without experience of Gmail).
Regardless, before I decided Inbox wasn’t for me I found the following blog post quite useful in sorting out the details of the Inbox functionality coming from a Gmail perspective: