Double-click can pose multiple problems... you can move the mouse too much between the 2 clicks and it won't register as a double-click... or worse, it will be interpreted as a "drag"... same problem with waiting too long between clicks. It seems that double-click only originated due to the long-ago hardware limitation of having only 1 button on a mouse. Is it time to "retire" double-click from our user interfaces?
Strictly speaking, double click hasn't been necessary since Windows 98 allowed users to single-click desktop icons. It just never caught on...even after 14 years of interface evolution.
So why has it remained? Custom (as you know, since you've tagged this question
convention). You have to respond to users' expectations, and the majority of users are accustomed to single-click-select and double-click-activate for things that fall into the same taxonomy as desktop icons (i.e., things that can be moved or have subsequent actions invoked upon them).
The reason for this is presumably that users have internalized the concept of click-to-activate, and they define activation differently for each given type of item. A file on the desktop can have a myriad of actions performed on it once it is focused (anything in the context menu). A button (usually) can't: it just fires whatever action it's bound to.
So, a desktop icon's "activation" is selection, and a button, hyperlink, etc is do the thing the button's icon represents.
That said, I have seen a few technologically-disinclined people double-click hyperlinks.
Double-clicks are rather hard both to discover and to execute, and many less computer-literate people still struggle with the concept. I often see people double-clicking on links or other single-click widgets, just because they've learned once that "double-clicking is for execution, while single-clicking is for marking and selecting". This is still largely true for operating systems such as Windows, OSX or Linux (desktops), but weakens with concepts of web applications - which already mostly come without double-clicks - spilling over.
In my eyes, the best chance of getting rid of the double-click is the continuing spread of web applications. Once their single-click paradigm spills over to operating systems enough to change default behaviors there, we can start thinking about retiring double-clicks.
While the number of NUI devices increases and GUI devices decreases double click will definitively begin to disappear. Double click definitively has its place as it imply users intent to click objects "icon, link, etc ...". This intent has been replaces with touch in modern NUI devices.
Double clicks forced retirement will appear when the number of touch devices completely overcomes those that require the mouse. Time will only tell.