I've just finished the first rails tutorial and now want to learn something about how other developers use it. So is it possible to "read" rails web applications to learn about its architecture and design?
One of the better ways I've found to really get into the "meat" of a Rails app is to go to Github and find some of the Rails demo/example applications that people put up there; there are even some fully-featured applications (FatFreeCRM comes to mind) but be aware these are usually anything but simple and I would not recommend a beginner who just has an intro tutorial under their belt to dive into, say, FatFreeCRM. There should be a plethora of similar but lighter-weight apps floating around Github; just as others have said be mindful of the date/version they were using as a lot has changed in Rails in the various versions.
Try to find an application that has a full suite of tests (or specs), so you can at the least follow the tests to get an overall approach of the application, and this will also train you for a career as a professional Rails developer as if you were brought onto an existing Rails app as a new developer, chances are you would "learn the guts" of the app by reading through the tests/specs.
I am not sure exactly what you mean, but if you didn't do this tutorial, I would highly recommend this: Ruby on Rails Tutorial
You build an application and learn a lot of details on how to think about the application.
It's certainly a good idea to read other people's code, and you will probably be able to understand most of what a Rails app does, but also beware of picking up bad habits or out-dated approaches.