PPCoin - I have tried to read and understand this. However, so far, I don't understand why this is better. I thought they wanted mining to be hard to do.
Well, "better" is subjective, but with proof-of-stake, coin ownership is used to achieve consensus instead of hashing power. A 51% attack would require the attacker to have 51% of the coins, instead of 51% of hashing power in proof-of-work. I'm not sure which is harder.