Political Intrigue: Rare in my games. This could be any situation where there is conflict with characters or groups that has not been combat (or there can't be combat). As an example, the King's adviser has taken a dislike to the party's paladin and tries to frame him for crime. Or maybe the prince has hired party to discover who is behind his arranged marriage to the head of the Thieve's Guild's daughter. Hard to script much out in advance and the GM must think quickly to fill in plot holes discovered by the party.
Plot/Story: Is there anything going on besides a series of unrelated adventures? Were the cultists related to the dragon? Is the town just a place to buy new gear or do things change. As a GM I personally like this part of the game. I like to create personalities that I can use to deliver story elements. The story might be be just one layer or many depending on the GM or the players. Crossroads, my current campaign, has many layers but only a few have really come to light. The one thing about this element is that many players could resent the plot being imposed upon their story. Overheard at the table, "ok, we are waiting for the plot train to go by before we cross".
Power: Your character wants to be the biggest, baddest and strongest. This is something that the GM cannot know unless his player(s) tell him. Any class could be motivated this way. Maybe the character wishes to be a Guildmaster, Warlord, Mayor or General. Anything that brings this character closer to this goal is interesting, everything else is a drag.
This can be a really tough one for the GM. Especially when one player has these aspirations and the others are into puzzles. This situation would fit right into Combat and Story oriented games. Say one character wishes to be Regent, the GM would add that to the story and the other players simply provide combat support to make things happen.
Exploration: To boldly go where no one had gone before. Prowling into the deep, dark recesses of the planet or sailing to isolated islands to find cliffs of crystal. You want to go to different places in the world and see what is there. You have little interest in intrigue and story is more of a travel log.
What do you as a player enjoy? Had you ever thought about it before? If so, had you ever talked to your GM about what it is that motivates you in the game? If not, you should. Knowing what kind of game your players want would make creating a game they'll like a lot easier.