It's not as good as the Android app or the regular website but it is usable in a pinch. In fact, the mobile version of Google Reader looks like it was built by an intern in 2005 and then forgotten when the intern was hired away by Facebook. But it works.
I only wish I could say the same about the Kindle Cloud Reader. This will not run on the Nook Tablet, darnit - not yet, anyway.
The 6 apps I found are:
The first 2 items on this list are library ebook providers. One is the dominant distributor in the market and the other is still working to sign its first hundred or so library partners.
Pulse is a news aggregator app which pulls content together from any number of predefined channels. It's immensely popular on Android and recently expanded to a browser version which works on PCs.
Instapaper and Readability are 2 services which let you save web content for later. These apps can tie in to your existing account with the respective service and receive that content. Instapaper is not free, but Readability is.
And for my last app I am sharing an app which isn't an app. Ibis Reader is an HTML5 based reading app which runs in the Nook Tablet's web browser. It supports Epub and doesn't do anything that the Nook Tablet's own reading app can't also do, but I'm including this app in the list as a reminder.
There are a lot of web based services which should work on the Nook platform. Just because B&N restricts which apps get into the Nook App Store doesn't mean you can't try to get around their restrictions.
P.S. If you know of an app which isn't listed here but works on the Nook Tablet, please leave a comment.