Edit:
New Icon:

Banner:

Source files: graphics.zip
Old post:
I saw some pull requests about this recently so I gave it a try:

It's kind of tricky to stick with the robot dog design and this is the best I could come up with. I'd also be happy to visualize some other ideas or chnage some aspects of the icon.
If you like it say the word and I'll create a pull request with all the files ; )
From an user perspective: looks very nice. :)
A couple of thoughts:
My issue with adding the antennas was that it doesn't really look like a dog anymore. I tried to strip it down to the most recognizable elements in order to put some focus on the email part. Maybe a different shape will help. I'll post as soon as I get something that looks decent :)
I love your icon idea! Especially the envelope eyes.
Consider simplifying it even more by using only the eyes and nose. Horizontal lines can be added to make it more unique and K-9 like, as can be seen here: https://goo.gl/images/kRF55v
Here is an amazing example of what I'm thinking, so you can see it in its full glory. :D

I actually like this icon! My first thought was about the aspect ratio as well. Does that work as a square?
I don't really care about the antenna ears - in fact when cketti mentioned it, I had to check out the current k9 icon because I had never consciously perceived the antennas.
I just realized, K-9 Mail already has a pretty mail icon - in the widget.
I think all it needs is the top half colored K-9 Red and the bottom K-9 Gray.
I find this new version great.
I allready changed the default icon to it using Nova. Thanks !
How about this?

Both the first post squared version and this latest rounded version look really great to me, even if they don't have the antennae for ears. Just my $0.02

I made this one for my private use.
I also made a feature graphic matching the design of the icon:

This is really getting somewhere.
Asking for a friend, would you put the source online so others can dabble with it?
Sure, here you go:
We're working on K9 for a university project, and most of the participants in our user studies complained about the icon (mostly about it being ugly and incomprehensible because it's not clear how it is related to email). In order to address these issues we tried to simplify and modernize the icon a bit.

This is just a concept, but if there's interest we can polish it and do a PR with all the necessary assets.
Here's a little comp to show how it would look on the homescreen:

I have to admit that so far I'm not in love with any of the proposals. But I do like the work by @moctodot and bertob. Also, @Valodim pointed out to me that we don't have to find the perfect icon right away. The proposed icons are a better fit than what we currently have :)
So for the next major K-9 Mail version I'd like to go with bertob's icon.
@bertob: We'd love to get a pull request. Please make sure the icon follows the material design guidelines for launcher icons as closely as possible, especially regarding size/padding.
Thank you to everyone who took the time to create one or more icon proposals. You are awesome!
Please keep the suggestions coming.
As a quick introduction on how to do material design icons I found the following video quite helpful: https://www.youtube.com/watch?v=GiFV-xfW9pk
@cketti, thanks for the video link, that was very helpful, since the official documentation is not very detailed on some things.

I have redrawn the icon and adapted it a bit, trying to follow the icon grid and the rules for shadows and highlights as closely as possible.

Pull request here: #2082
Here's another concept:

Indeed Moctodot's version is the only one I even like (simple, material, beautiful), nothing against bertob's work, it looks good, just too clutered and not material / minimalistic enough in my opinion...
While changing the icon, would a "materializing" be possible for the app itself ? There is a fork on xda which does this quite well without getting to deep into changes, but play store updates are great...
Just my 2 cents.
@skieffer, how is this material ? ;)
A complete material design rework of the app (or the discussion of it) is already in progress. #1859
Hey everyone! Just a heads up. I've updated and released my 2013 redesign project into a separate repo you can find here: https://github.com/k9mail/k-9-design
It already includes user testing, high fidelity design for all screens, color themes, icon (in all sizes and optically corrected to fit a variety of devices and wallpaper colors), etc. @moctodot + other designers in this thread - feel free to contribute to it! Right now the biggest remaining ask is a centralized style guide, documentation, and annotating existing screens.
Most helpful comment
How about this?