When I was little, my parents gave me a book of observation, or hidden object, games. Looking at a detailed, black-and-white pencil sketch, I'd have to find dozens of objects hidden within the scene. It was much like this game, except the list of objects was printed small in the back of the book (meaning I was supposed to attempt to find every object without the list, then use the list to test myself). Where's Waldo? is probably the most popular hidden object game.
Observation is often a component of larger gameplay. In football, most of a quarterback's job is observation. He must try to read the defense's strategy. He must know how his line is holding up against the defensive linemen, know if the linebackers are rushing. The QB must be aware of how well or poorly his receivers are beating coverage, where the holes are, where the best players are on the field. Quarterbacking is the most difficult position in football because the quarterback must observe a dozen things at once and respond immediately.
Observation in detective games focuses on relevance and patterns. Why is a door ajar or a window unlocked? Does a tear or injury suggest a conflict? Not all visual elements and lines of dialogue are relevant in a good detective game, so the player must pay attention to everything and be able to remember details when something relative emerges. Most clues aren't clues until a related object or event gives them significance.
Timing is an observation skill. The player must recognize a pattern to adjust to that pattern. Firing mortars on a moving target has always been a lot of fun for me. It involves judging the speed of the missile, distance, speed of the target, obstructions, and likely adjustments the target will make to its current path. It's much like quarterbacking... knowing when and where the receiver will turn, where the defenders will be at release and where they can get to while the ball is in the air, as well as terrain slickness, wind, and other factors.
How else is observation included in games? Surely, it hasn't all be done before. What's some new play on observation a game might use?