lady_morana,
Be aware that most e-reading software is FREE to download and install, including the most popular ones like
Mobipocket,
eReader and
MS Reader. You'll pay for e-books only, and if you look in places (like this site), you can find e-books available for free. (My books site also has a free anthology of short stories to download.)
Otherwise, it sounds like you're talking about simply reading a book from your web browser. Take a look around for the e-book sites that offer the entire book's text online (usually for free), and you can do that. There won't be too many pay sites that will allow you to read from your browser, beyond a chapter or so.
I seem to remember some sites that packaged the e-book with its own built-in proprietary reader software, but I don't know if any of them are still active. This would be, in effect, allowing them to automatically install their reader on your PC, so it might not be what you want... unless the only reason you don't want to install reader software, is that you don't want to have to physically do the install yourself.