After seeing Divvy on the Mac, I was envious as a recent migrant from Windows XP to Ubuntu. Fortunately, I found Compiz as a window manager. From the Ubuntu terminal (Applications > Accessories > Terminal), install Compviz if you do not have it already.

sudo apt-get install compiz compizconfig-settings-manager compiz-fusion-plugins-extra".  

What you're doing here is running the program 'apt-get' with superuser privileges (sudo). You're also telling 'apt-get' to install 3 software packages from online sources 1) compiz 2) compizconfig-settings-manager 3) compiz-fusion-plugins-extra.

Open Compiz (System > CompizConfig Settings Manager). Ensure 'grid' functionality is enabled. 'Grid' is located under the "Window Management" section.*

The settings enable you to resize windows by holding CTRL + SHIFT + (1-9 on the keypad).

1 - top left (1/4 screen) 2 - top screen (1/2 screen 3 - top right (1/4 screen) 4 - left (1/2 screen) 5 - full (full screen) 6 - right (1/2 screen) 7 - bottom left (1/4 screen) 8 - bottom (1/2 screen) 9 - bottom right (1/4 screen) * You can also use the Filter in the Settings Manager and type "grid".