Searched google for "words with friends battery life" and this is the first post. It's killing my Dinc battery, and if I don't remember to exit back to the homescreen before turning the screen off, my phone will get warm and the battery will get killed. It seems like whatever this app is doing, it's doing it constantly and causing CPU activity to spike up to 100% until I exit the app, according to System Monitor. When I check "Device Usage" that's only at 100% when I was playing, but the CPU activity stays spiked no matter what, as long as the app is the last thing active prior to turning the screen off.
EDIT: Well, I tried turning off the notifications completely, I really couldn't care less about them anyways (I just check the game when I get a moment and the notifications didn't seem to be 100% working in the first place), and it looks like there is no longer 100% CPU activity with keeping WWF open and the phone sleeping. So it looks like the culprit here was indeed the push notification system WWF uses. At least that was an easy fix!
EDIT 2: Ok, well it looks like that didn't help, the battery is still being chewed apart if an actual game is left open with the phone sleeping, just not the home page of the game. So I guess you just need to be diligent with making sure you back out of a game with someone prior to letting the screen turn off.