I use one such application and it is great. It is called GridMove. It starts with Windows (but only if you tell it to). When you hit Windows+G, it shows you the current monitor layout with the places where the window would go, with a number in each. You type this number on your keyboard and the window goes there, resized to the size of the place. Or you can also drag the window.
It comes with a few grid layouts preinstalled, but you can download more. There is a thread in their forum which lists additional layouts. Or you can write your own layout. It is done in a text file with a pretty intuitive syntax, and you can open the ready layouts to use as examples, so I found it very easy.
Another plus: you can have different layouts on different monitors. Very good if you have one small laptop monitor which can only show two vertical windows in a usable size, and a big external monitor where you can have three windows vertically.
The only disadvantage I've seen so far: you cannot group windows. So if you use an application which has several floating toolbars like Gimp with Brushes and Layers, you cannot move them together to occupy a square spot, but have to write them their own small spots into the layout and move them separately.
All this goodness is available as free and open source software and doesn't install any annoying browser toolbars etc.
You can get it here. Hope you like it!