Update: I was unfortunately not aware of Shamus Young's severe criticism of Fallout 3 available here to link in the original piece and I regret that. It dovetails rather nicely with what I've written and it's much better executed than my piece. I strongly recommend anyone...
While looking at your Springfield in the game, find Homer Simpson. He's the very first character your unlock, so you should know him by now. Tap on Homer so that his activity list opens. At this point, tap on Homer 10 times. If you've done it correctly, a message will appear and reward you with 10 extra donuts.
2) Mayan God Trivia
In the recent Halloween update, Springfielders (Springfieldians?) can earn free donuts by answering the Mayan God's trivia question correctly on the first try. You don't need to watch the Treehouse of Terror episode to get this one right… the answer is "The Zune."
3) Level Up FAST
In order to earn more free donuts, you'll have to rely on the small rewards you get when you level up in-game. Each new level typically brings one donut. If you want to know how to level up quickly, check out our Simpsons: Tapped Out level up guide.