Speaking from the United States, our system of Constitutional Republicanism -- or Representative Democracy -- has worked better than most around the world. Pure Democracy tends to become tyranny as a majority becomes too influential; Communism, as mentioned in #3, is essentially dictatorship, and so is easily corrupted; Socialism tries to ensure equality by forcing workers to produce for both themselves and non-workers, and the result is always that the workers cannot keep up with demand. By implementing checks and balances into the basic law, the U.S. has, by and large, avoided the major pitfalls of past governmental systems.
No chance. We've seen governments of all sorts in the history of the world and none of them has come anywhere close. Human nature will not allow this. There are always going to be people who want to commit crimes. There will always be people who hate others for some reason or other. There will always be people who are not lucky enough or not talented enough or not hard-working enough to get ahead. A government can minimize these things, but we will never be anywhere close to free of them.
I agree with post 2 that we do not currently have any system of government that has solved the problems of poverty, injustice, crime, and discrimination. Each system seeks to end these problems in their own way. Democracy allows the people to have a voice in how these problems are addressed. A democratic government addresses poverty through tax payer funded programs. The tax payers have a say in electing officials that will determine how these programs are organized. Democracy also seeks to deal with injustice, crime, and discrimination through a series of laws. Democratic citizens have a say in these laws and the system that creates them. Socialism takes a similar approach but with a different twist. For example, many socialist countries have higher taxes to fund universal health care. Those less fortunate are still able to have food, shelter, and access to medical personnel. Communism does not allow citizens to have a say in their government. If the communist leader is effective, the society will take steps towards solving these problems. Unfortunately, no form of government has found an effective solution yet.