Pie menus address many of the complaints of this slashdot article, and they've been around a long time.

I'll start by comparing screen corners to pie menus:

To quote Tog on Fitts' Law: "The time to acquire a target is a function of the distance to and size of the target." He points out that "the screen edge is, for all practical purposes, infinitely deep."

But the advantage of "screen corners" is just an indirect and wasteful application of Fitts' Law, which pie menus exploit much more directly, efficiently and flexibly than "screen corners". Tog's "screen corner" argument is just an ex post facto application of Fitts' Law: an after-the-fact rationalization, not the reason they originally designed the menu bar that way. If Fitts' Law was really the reason Apple designed their menu bar that way, then why aren't there four menu bars, one at each edge of the screen? Apple never mentioned Fitts' Law in their infamous menu bar patent.

Pie menus "slices" are better than "screen corners" or "menu bars" because:

Screen corners and edges are static and fixed in number, so they only enable a small fixed number of global commands at once.

Pie menus are dynamic and context sensitive, so each pie menu can have multiple slices, with a different set of functions associated with each, including submenus. The screen only has four corners and four edges, but pie menus are extremely reliable with eight items, and can support up to 12 items reliably.

Pie menus also support submenus, so you can have an infinite combination of pie menu items, depending on the context you click on, instead of just four screen corners or four menu bars.

Each pie menu item is easier to hit than any screen corner, because every pie slice target area starts directly adjacent to the cursor and extends all the way out to the screen edge, and beyond!

Screen corners and menu bars flaunt Fitts' Law by requiring you to physically move the mouse a large distance, and they usually leave the cursor far away from the object you're manipulating.

Pie menu target area "slices" extend all the way out to the edge of the screen and beyond, so their area is quite large, but you don't have to actually move all the way to the screen edge to select them. You simply move the cursor outside of the small inactive area in the pie menu center. Each "slice" target area starts out directly adjacent to the cursor, in a different direction, and occupies a large area extending out to the edge of the screen.

Fitts' Law relates the target seek time and error rate to the target area and distance from the cursor. The bigger the target and the closer the target, the faster the seletion and fewer errors. Pie menus maximize the target area and minimize the target distance, so consequently they minimize both the speed and error rate, as Fitts' Law predicts.

Pie menus have been empirically proven to be 20% faster than the linear menus, and about half the error rate ("A Comparative Analysis of Pie Menu Performance"; by Jack Callahan, Don Hopkins, Mark Weiser, and Ben Shneiderman; Proc. CHI'88 conference, Washington D.C.)

Screen corners are worse than pie menus, because they actually have smaller target areas than pie menu slices, and actually maximize the distance from the cursor by putting the target as far away from the cursor as possible.

Tog claims the screen edge target area is "infinitely deep", but in practice you never move the cursor an infinite distance, so you could never hit most of that infinite area, therefore it's only worth talking about the target area within a few feet of the screen, where you could move the cursor without picking up and repositioning the mouse.

Fitts' Law says that the bigger a target of a given distance, the easier it is to hit. But screen edge targets flaunt Fitts' Law by excluding the large target area of the entire screen itself, which always contains the cursor, while pie menu target areas start right next to the cursor, and extend out to the edge of the screen and beyond. Pie menus have larger target areas than screen corners, and those areas are much closer to the cursor. Therefore pie menus are more convenient, faster, and less error-prone, because require much less movement to hit their larger, closer targets.

Fitts' Law also says the closer a target of a given size is to the cursor, the easier it is to hit. But screen edge targets flaunt Fitts' Law by all being far away from the cursor, and leaving your cursor far away from the middle of the screen or whever you were before you issued the command, which is the most likely place you need to point next.

Pie menus exploit "locality of reference", so they don't take you away from where you're working, only to return there again and again. For example, they're great for selecting SimCity editing tools, because you don't have to move the cursor between the map and the tool pallette to select bulldozer, clear out some rubble, select road, pave a road, select wire, put up a power line, etc.