Yes I just watched 300...
But it still stands, what would a Roman or Greek army do to train their bodies for war?
A Roman and a Greek army were two very different entities.
A Greek army would have been made up mostly of levies that were called upon when needed. It was, however, a civic duty to keep in shape in case the state was at war. In Athens, for example, men would lift rocks in public in the gymnasium. Sparta, of course, was different. From the age of seven, he was put into an agoge where he would have extensive military training. However, keep in mind that according to some estimates the male population of Sparta's territories was 20% Spartan and 80% helot. But those Spartans who graduated from the agoge at 30 would have been in impeccable shape.
Rome was different. Originally the men were called up, much like in ancient Greece, and Livy references this many times, and one can imagine that their civic duties were similar to the Greek's. The Roman army of the 1st Century AD, however, was very different. It was a professional army. Vegetius goes into a significant amount of detail about this. A Roman soldier would march or miles in full armour and kit, for example, and this allowed the Romans to march incredible distances in short amounts of time (along with their road network, of course). They would fight with weighted weapons to train their bodies to be able to use the real thing very easily.
Keep in mind though that the ancient armies of Greece and Rome would focus a lot of teamwork rather than the individual leaping found in 300.
This is a surprisingly popular question, so there are a couple of different areas of the FAQ that might be helpful.