In D&D, as adventuring groups adventure, they grow more and more powerful over time. After a certain point, it may seem to the DM that no matter what he throws at the party, they hack it to bits with little difficulty. At this point, the DM is faced with a choice: he either forces the characters to retire and start over with first level characters, or he can change strategy completely. Most adventures (even the low-level ones), if they are good adventures, have a certain degree of mystery to them. One option for a DM of high-level characters is to take this element of mystery and make it the focus of the adventure.
Low-level characters can be guided from clue to clue by a DM, so the storyline follows a, more or less, linear direction until the mystery is solved. With high-level characters one may find it necessary to “throw them to the wolves.” Scatter the clues randomly about so there is no pre-defined order in finding them. Clues should be inaccessible to magic unless the DM wants otherwise. The final confrontation in a low-level campaign often involves a battle with the “head bad guy” and his cronies. If one assumes that the high-level party can kill absolutely anything the DM can throw at it, then perhaps a climactic battle is not the way to go. Perhaps the climax should be something more akin to a detective novel where the killer is unmasked and taken away, but with little violence.
Another option for high-level characters is political intrigue. High-level characters often have significant landholdings, even titles, and therefore have certain responsibilities towards their kingdom. Because of this, political happenings should affect them. For long campaigns, one could use a mass combat system to run an epic scale battle where the characters act as generals and thus face the challenge of commanding troops in battle. Although the characters still have a vast arsenal of spells, abilities, and weapons, they may lead an army of peasant warriors who do not. And what good is victory, if all your subjects are slain?
Finally, one can mix politics and mystery. For example, suppose the party learns that there is a conspiracy to assassinate the king. If one focuses the adventure on politics, then they must use their political resources to identify the conspirators and foil the plot. Almost all adventurers have trekked through the labyrinthine depths of a forgotten dungeon. But what about visiting a noble’s costume ball to gather information on suspected treason? Again, the use of magic should be carefully limited. There’s no mystery or challenge when all the characters have to do is commune with a god or goddess for an easy answer.