Hardly any? That's been a minor trend in web sites for a while, but changing scroll behaviour for no good reason is widely regarded as an antipattern by UI professionals. I don't recall ever seeing normal scrolling behaviour subverted in anything I'd call a web application.
or the back button
This is a tricky one from a usability perspective, because some users see URLs as shortcuts to particular parts of a web application and expect the back button to behave accordingly as they navigate information in the app, while others think of the whole application as being a single page and expect the back button to just leave everything. But there is a whole set of browser APIs for managing that behaviour, and it's something a well-designed application will at least present in a consistent and logical way.
or the ability to middle-click on a link and get a new tab
This sounds like you're talking more about web sites than applications again, and again it also sounds like you're talking about bad design that web UI professionals would universally disagree with. It's usually caused by newbies who read some style-over-substance tutorial and decided that making links or buttons with elements other than the designated anchor and button ones that exist for that purpose was a good idea. After the first few glaring usability problems, they'll learn better.
or the ability to highlight text.
I don't really understand this one at all. The only times you wouldn't be able to highlight text in a web application would be if the designers have actively prevented it, for example to prevent selecting UI labels along with the content of a text field. This typically works exactly the same way as any native desktop application.
But in spite of that, nobody ever really expects drag and drop or rich copy and paste or any other data exchange mechanism to work between web apps.
I don't know what you mean here, either. Dragging and dropping text between web applications typically works fine. If by "rich copy and paste" you mean other more complicated data types, what happens is obviously highly context specific, but once again, this is the same story on native desktop applications. It's not as if you can copy a selection of spreadsheet cells and paste them into a drawing package with obvious and meaningful results either.
As a final comment, the examples you're talking about here all seem very "meta". As such, they're not particularly interesting to me, because as a UI developer working on a web app you generally get the expected behaviour by default with these kinds of things. Sure, some people can and do break them. They're just bad UI designers. Some people make native applications with shocking pink skins over the normal window dressing, too, but that doesn't mean all native apps are bad.
That "and by extension web apps" bit is completely wrong. The long-standing conventions of how web sites work are mostly irrelevant to fancy web apps, and to the extent that they are relevant, web apps break them left and right. Just look at how many web sites/apps hijack or break scrolling or the back button or the ability to middle-click on a link and get a new tab or the ability to highlight text. Web apps are all about breaking the usability standards for web sites and replacing them with a bastardized version of the usability conventions from various native OS toolkits. But in spite of that, nobody ever really expects drag and drop or rich copy and paste or any other data exchange mechanism to work between web apps.