*Since lever classes aren't all that important, I'm not going to define them; see Wikipedia or some other source if you'd like more information.
There are three main jobs a lever can do as a trigger: block, yank, or tap. A catch blocks another object from moving until more pressure is applied. For example, a trap door in the floor might have a catch keeping it closed until it is pulled open by a wire being tugged, or until it gives way under too much weight. Or the catch is normally open, but another trigger pulls it closed, blocking a door. You could, for example, have a hefty metal bar on an axle next to a door; if one end of the bar is pulled away from the door, the bar turns so that the other end blocks the door, keeping it from opening all the way. Place this bar and axle assembly above a door and attach a chain to one end that runs through pulleys, connecting to a trigger on the other side of the door, and you have an entrance that can be sealed after a room is entered. This can be circumvented by not allowing the door to close, or not allowing the bar to turn, perhaps with the use of spikes.
A tripwire yanks another trigger or an object when the lever is moved, or the lever does the yanking; the wire itself is really just an extension of one end of the lever, or acts as a lever itself. One example is a lever mounted on a door frame so that opening the door moves the lever, yanking a wire. The direction the wire is yanked depends on how the lever is mounted (fulcrum in the middle, fulcrum on one end) and where the wire is connected. The tripwire can run across the ceiling of the room where it is located to trigger something else (pull the trigger on a crossbow, for example,) or it can run through a hole in the wall and across the ceiling of the corridor on the other side of the door, perhaps triggering a trap behind the adventurers opening the door. If one end of lever is flush with the door and a spring under tension keeps it pressed against the door, the lever can even be on the side opposite the direction the door opens, which makes tripwires on doors very versatile.
As an aside: Richard brought up in a comment the idea of traps that haven't been "plumbed in", in other words were added after the original construction was finished. Unless the inhabitants have only moved in recently, though, or are loathe to do construction themselves, the main guts of a trap can always be hidden with false ceilings, walls, and floors, which create instant ducts and chambers for tripwires and gears; a dwarf will automatically detect this new construction. There needs to be some kind of opening (perhaps shuttered) for the deployment of the "payload", and the other end of the trigger or series of triggers needs to be exposed or connected to something that is exposed, so that adventurers can trigger it. The tripwire and spring combo mentioned above can be hidden quite well, unlike some of the other triggers mentioned in the series so far; carve a hole in the frame of a door or lip of a container so that the door or lid covers the hole, then place the lever and spring in the hole, so that opening the door or lid allows the spring to push the lever out, triggering the trap. This kind of trigger would be very difficult to detect, so use it sparingly, unless you want to provoke player outrage.
A hammer trigger hits or touches another object when the lever is moved. Levers used as compression triggers to break some object would be one example, but the intention can be something else entirely; for example, a hammer trigger could strike a bell, to act as an alarm, or it can push a bar in a groove, to bar a door. The giant electric switches in old mad scientist films are another example; moving the lever causes the metal part to touch a metal plate, completing an electric circuit. Going back to more violent uses, a hammer striking an object can be another method of launching a projectile; perhaps a trigger on a door is linked to multiple hammer triggers in the form of mounted croquet mallets, which hit balls across the room to create obstacles to trip over.
Lever triggers are visible if an adventurer can see the location where the trigger is located. Levers on the other sides of doors can't be seen without magic, of course, but sliding a blade between a door and its frame might contact the lever, and might even reveal a hollow in the frame itself. Disabling levers generally involves wedging something in between the lever and the direction it moves towards; the iron spike can be your friend, here, as it could even disable the hidden spring and lever trap mentioned earlier. If a lever moves something else through some kind of channel or groove, the channel itself can be blocked.