Three classic examples from Chinese stories are:
1. Defeat/remove the corrupt - sometimes the Emperor, more often corrupt officials. The adventurers must track down the source of the corruption that is ruining their lives, defeat it, find the next step(s) in the conspiracy and (after however many steps are desired) finally defeat it to restore order and prosperity to the Empire - Jade Empire, the Bioware cRPG, is an example.
2. Unite the empire and bring peace/prosperity. For whatever reason the Empire is no more, and you wish to restore/create it. Plenty of overcoming warlords, politicking, and the domain-game is in play as well. Romance of the Three Kingdoms fits this, to some degree.
3. The Empire needs something. Go and get it wherever it is, which might mean travelling to strange foreign lands, into the depths of magical lands within the empire, even into the hells or heavens to obtain it. Journey to the West is a classic example.