Hypertxt allows you to view your plain text files in the browser, with some support for rendering markup languages like Markdown. It can serve text files in a hierarchy of directories rooted at a given directory.
You need the Flask web microframework.
$ [sudo] easy_install flask
Start by pointing Hypertxt to your document root (the directory containing your text files). Optionally, select the port at which Hypertxt listens for connectios (default=8080).
$ python hypertxt.py --root <document-root>
Your text files can be viewed at http://localhost:8080/