People kept complaining about Anakin turning to the dark side way to quickly, which I admit, the first time it did seem awkward.
But now I realise that, after all the building up, and the way Anakin's head works, it's really no surprise that he went so quickly.
Allow me to explain: In Episode 2, which takes place 3 years before Episode 3, we can already clearly see that Anakin is becoming evil. He basically has all the personallity traits that will lead to the dark side. He's cocky, sarcastic, rude, angry, afraid and he has one creepy temper.
In the Clone Wars cartoon, we can see even more that he's going to the dark side. Again, he has all the personallity traits, and you can actually tell they're getting worse. Then, he goes into a furious rage on Yavin 4 where he kills what's her name (the Sith assassin). And then in the second season of Clone Wars, you see how the lie of him and Padme is tearing him apart inside. He wants to shout their love from the roof tops, but knows if he does that, he'll not only ruin his life, but her's aswell.
Now, his mother has died, he's living a lie, he already has a pretty screwed up personallity, he's very angry and frustrated and he's already very close to turning to the dark side on his own, without Palpatine's help.
It's obvious how Anakin thinks. Padme is the number one thing on his mind at all times. Remember one of the first things he says in Episode 2? He thought about her every day the entire time they were apart. He's always thinking of her. Another thing he's always thinking about and wanting is power. He's always talking about how he should be better, and how he should be stronger. He wants to be better than all the other Jedi.
So, if we take all this into consideration, when the fear of losing the main thing he cares about comes into the picture, and he's being lied to and manipulated by Palpatine and the very strong powers of the dark side (I remind you that Luke almost fell to the dark side aswell, when he cut off Vader's arm in his fit of rage), it's really no surprise at all that he'd do anything to get the power he wants and feels he needs. Then once he's submitted to the dark side, it just eats him up right away and makes him do things he never would of wanted to do. Once Anakin puts on the leash, Palpatine takes him for a long, long walk.