Even within this context, icons have been used for a long time in things like toolbars. But historically they've been quite descriptive of what they do, and often times have been accompanied by a textual description if there's any uncertainty as to their meaning.
Like the earlier commenter wrote, however, we've seen the use of icons really taken to a stupid extreme as of late. This is especially true when it comes to websites and web apps. The icons are often rather abstract, to the point of causing confusion and harming usability.
Even desktop apps have succumbed to this. Look at Chrome's menu icon. In the last version I used, it was a stack of three horizontal lines. At a glance, it's not clear at all what it represents. It's only after clicking it, and seeing the menu that opens, that the connection is made.
That isn't what we see with most web apps these days, including the major ones. There's continual change, including the icons that are used, where they're positioned, and what happens when they're clicked on. If you discover what an icon means and does today, there's a very good chance it'll have changed by tomorrow, if it's even still around.
We're much better off losing a small amount of space, but getting an obvious and unambiguous description when text is used instead of icons.
Text works just fine in most applications, because the shape of a particular word is itself iconography.
> fad [of replacing text links with icon-only buttons in software UI]
You realize that iconography predates all civilization, right?