I think Plato's biggest legacy that he has left us with is his idea of democracy and government. Although, as #2 identifies, the government we are lumbered with today is not exactly the same, really Plato can be seen arguably as the "father" of democracy in his outline for society and the way it should be run.
The idea of whether or not there is a transcendental notion of the good to which we should aspire is a powerful concept. On one level, Plato's discussion of the "forms" and the "ideals" to which all human endeavor should be geared can pull someone to aspire to the highest of goods. Yet, at the same time, this can be manipulated by those who wish to consolidate their own power and eliminate other notions of the good. Hence, the reality is that in order to prevent some type of force from coopting the public good through the invocation of the "forms," a settling for diversity and divergent paths that might not lead to these forms may result. I think that it is really interesting to put Platonic thought in the modern setting with all that has been experienced in terms of singular pursuits of what had been called "the forms," which was actually far from it.
One of Plato's ideas that I find of particular relevance today is the role of the father and son. He seemed to insinuate that the son's life success is dependent on the father's influence, interaction, and interest in the boy. This makes great sense because so many children look for their self worth in the parents.
If you take a look at how the family has broken down in society today, this question of influence is a valid topic. My son finds extreme value in learning to become a man from his father. We also see great examples in society of what has happened when boys are missing fathers. There are indeed many great single moms out there doing great work, but Plato noticed something about this relationship and repeatedly brought it into his writings.
His ideas about government are close to ours, however our employment of democracy is not exactly the same as Athenian democracy. He saw a 3-branch government similar to ours which includes those who reason well and have great capacity for wisdom, those who secure our safety, and those who produce for the benefit of the people. This doesn't exactly mirror our executive, judicial, and legislative branches, but it does mirror the structure of a democracy. There are people who work for the benefit of others, there are policing and law-inducing groups, and there is a body of politicians who should be wise. I would say this balance between the groups should generally push for the betterment of a society and even when one is off base a little, the others reel it in. I see this at work in the outrage of so many Americans today with government spending.
I've always appreciated Plato's concept of justice. It is not to be decided by the few or the strong, and it is always good for the whole. Our system of justice falls short, sometimes, but it does strive to follow Plato's concept.