And based on my time with the T68, I think it offers the most options. It runs Android 4.0. That's a newer version of Android than you can find on most E-ink devices, and since it ships with Google Play you have the least hassle in finding and installing apps.
Here's a list of apps which have been tried by T68 Lynx owners and found to work.
Apps for Reading News Feeds, Articles, eBooks and More
Opera Mini - The T68 Lynx ships with the stock web browser; it works okay but I think we can do better. Google Play will tell you that Chrome and Firefox aren't compatible with the T68 Lynx, and sadly Opera Mobile tends to crash. But Opera Mini works, and it offers a better interface with an E-ink-friendly drop down menu, zoom buttons, and other improvements.
Feedly - eBooks are great, but I for one spend a lot of time following the news feeds of blogs and media sites. So do a lot of other T68 Lynx owners, and that's why they installed Feedly (I prefer to use a different service). The app works great, and when tied to Feedly's free reading plan it offers access to a near unlimited amount of reading material. (Just be sure to turn off background syncing and notifications if you want to conserve battery life.)
Gmail - When I said that you can read on the T68 Lynx, I didn't mean just ebooks. The Gmail app in Google Play can be installed on this ereader. It works just fine for me, and it even runs in the background just like it is supposed to. I've even used the onscreen keyboard to send a couple emails.
Kindle - What kind of a post would this be without mentioning the king of all ebook apps?
The Kindle app from Google Play installs and it works almost perfectly. You can read, buy ebooks, and take notes, but there is a catch. The Kindle app doesn't work with the page turn buttons, and there's no way to disable the page turn animation (trust me, we've tried) but on the plus side the Kindle app is faster at page turns than the ebook app which Onyx shipped on the T68 Lynx.
Moon+ Reader - Quite a few ebook apps work on the T68 Lynx (including Kobo, Aldiko, Alreader, and more) but I want to single out Moon+ Reader as your best option. Like the Kindle app it is faster than the stock reading app, and it also offers Dropbox integration and a theme that looks okay on a grayscale screen, and it even works with the page turn buttons. This is the ebook app you should be using, not the one that Onyx provides.
Scribd & Oyster - As a reader just reminded me, you can install the ebook apps for both of these ebook subscription services.
RepliGo, Adobe Reader, and ezPDF - The T68 Lynx already supports PDF out of the box, but don't let that stop you from installing additional PDF apps. All 3 of these apps work well on the T68 Lynx, and RepliGo works great. it offers an easy to read interface and calmly handles 200MB graphic novel PDFs. I don't think I am overselling it when I say that you should take a pass on that next cup of coffee and buy RepliGo instead. it's that good.
Pocket, Readability (& Instapaper?) - One lament shared by Nook Glow owners is that the offical clients for Readability and Pocket don't work on their device. But since the T68 Lynx runs a newer version of Android, you can run the official apps as well as third party apps. I have run both Pocket and Readability, but I can't speak for Instapaper. Google Play says it is compatible, but I can't find anyone who has tried it.
Comixology - I found that I preferred to read comics in RepliGo, but if you are really into comics then you'll be pleased to know that the Comixology app works. I only have a few titles with that service, but I was able to download them and read just fine.
Evernote - In case I haven't disabused of the idea that this is a mere ereader, Evernote is usable on the T68 Lynx.At the request of a reader I logged in and added notes to my long-dormant account. The T68 lacks a speaker or a mike, so some types of notes won't work, but you can review and add to your notes.
But Wait, There's More
I've only just touched the surface of what you can do with the T68 Lynx. There are other reading apps which you can install, and while you're in Google Play you might want to install utilities like ES File Explorer, Dropbox, and the like. Sure, you may be planning to use the T68 Lynx as an ereader but you will still need to manage it like you would an Android tablet.
So tell me, How do you like to read on the Android-based ereader?