I use it all the time, actually. In fact, I installed scripts on both Ubuntu and Mac that accomplishes the same thing. I use it all the time while programming. Half maximize VisualStudio/Eclipse/Xcode/Gedit/etc on the left side, and then my browser on the right side. Sometimes it's also really nice to be able to quickly pop a tab out of Chrome and quickly move it to fill perfectly the other half of the screen. I use this when posting content from one page onto a forum or something.
I've also used it a bunch while doing homework. Have Word open on one side, and whatever I'm reading on the otherside.
I was also a grader for school, and i would've hated life if I didn't have this feature. Having the key open on one side and then the student's assignment on the other half. When I open the next document, I quickly move it to the other side.
Anyway, as you can see. I love the feature.
Edit: posted at the same time.
Quote: "Start using the maximize window and alt+tab feature."
Hah! never. I hate having maximized windows.

And I understand what it takes to get windows to resize and I agree with you completely that not every website can do that.
But I'll use two that I notice it in the most as an example: TGC Forums and Apple's stupid developer website.
This forum is only stretched by ADs. Lame. I don't mind that a site advertises (in fact, I don't use adblock because I feel it's the website's right to advertise while giving me free content), but I do care if an ad is forcing my window to be a certain size. That can easily be fixed.
Apple's site is similar in that it's being resized out of sheer stupidity. Looking at it there are several places they can make more flexible. It's not that the site is doing anything remarkable that makes it difficult for them to accomplish this. It's that they just didn't care. (Which is the Apple way. "My way or the highway", but that's another story.)
Your mother has been erased by a mod because it's larger than 600x120