The rest of the time I would read the paper copy. I also print out longer articles to read - paper seems less fatiguing to read from than a screen.
The font, font size, column width, and line spacing seem to make a big difference with how tiring it is to read on the screen. The Free Culture PDF was one of the the easiest documents I've come across to read. The default WordPress and Blogger themes use similar column widths and line spacings - this suggests that there might be an optimum way to display text for readability.
This is a bit of a leap, but if you're designing a site that has a lot of paragraph-form text, mimicking the typography of a typical paperback will probably do a lot for your site's readability. Does anyone else have specific text formats that they prefer for reading on the screen?