Every e-book reader I have seen includes some type of web browser. Are there any that have no web browsing at all?
Yes, there are many, both software only and hardware ebook readers that don't include web browsing especially older models. For many hardware ebook readers it doesn't make sense to have a webbrowser because they have no touch screen and no virtual keyboard, making it impossible to specify a URL. Most of these devices have no way to connect to the internet that would be a requirement for webbrowsing. (E.g. the older (2007) sony devices).
For software ebook readers it often doesn't make much sense to try and compete with real webbrowsers, they are better of focussing on enhancing ebook related HTML display functionality.
Before the kindle formats and ePub there were other formats that were not HTML/XHTML based, such as PDF (but there were a few other with a more efficient format than either of those as well) and readers for those ebooks don't have a HTML rendering engine built in, and web browsing would not be a natural extension to that kind of renering engine at all.
I'm not exactly sure if you ask it for the sake of knowledge or if it is a feature that you don't want to have on your ereader because it could be a distraction. Assuming the latter, Kobo ereaders do have a web browser, but it is buried in the "beta features" section. It is very basic, nothing too full fledged, more useful to have a quick reference than doing your regular Web surfing. The only ways to get it in your way while reading is to manually go search for it, or, while highlighting a word, select "search with Google / Wikipedia ". That, IMHO, is a nice feature ti have at hand, and doesn't distract you too much.
I hope this answers your question.