Consider a gear with one tooth. The tooth is, in essence, a lever, which can be used to activate another trigger; the fact that it is mounted on the rim of a wheel means that, as the wheel rotates, the lever repeatedly activates the second trigger. As long as the wheel rotates at a constant rate, the duration between trigger activation events remains fixed.
Another use for a wheel is as part of a pulley, to magnify the force of a trigger, extend it, or change its direction. It can also be used to rewind or reset another part of the trap; a wheel with a crank handle that can be used to wind up a rope or chain can be used to manually raised a portcullis that has been dropped by a trigger.
One particular use for a pulley or spool system is as part of a gravity-powered delay or repeater. Start with a spool on an axle, with rope attached to the spool's hub; attach a weight to the other end of the rope and wind it up. Add a peg to one rim of the spool that is positioned to be stopped by a catch (lever trigger.) On the other rim, add a flexible bracket (spring) with a mallet connected to the end; place a bell within range of the mallet. When the catch is released, the weight pulls the rope, which spins the spool, which rotates the mallet, which repeatedly bangs the bell; the result is an alarm trap. Replace the mallet and bell in the alarm trap with sharp blades mounted on poles and you have a rotating blade trap.
If the wheel is actual a gear, or has a gear attached, it can be used with chains to drag an object, or with a toothed rail or long screw to extend a pole (for a thrusting spear trap, for example.) This would be one way to create the iconic "crushing walls trap": replace the mallet/bell in the alarm trap with a gear that meshes with a long screw; embed one end of the screw in a slab of some material. When the catch is released and the weight causes the wheel to spin, the screw is moved along a track, pushing the slab. The same principle can be used for walls in a maze that reconfigure themselves, or for elevators.
If a wheel has a hole in it, it can be used as a shutter or valve. When the wheel rotates, sometimes it will align with the hole in a container, like a reservoir filled with sand, and sometimes it will not align, blocking the hole. When the holes are aligned, sand pours through the openings.
Wheels can also be used in the delivery system (the trap effect, rather than the trigger.) For example, the wheel could be a grindstone; it would have to spin pretty fast to cause damage, though. Similarly, the wheel can be a turning platform with an upright slab on it, for another variation of the maze that reconfigures itself. A really big stone carved into a wheel shape can be placed on a ramp with a wedge or catch underneath the front end; when the wedge is removed by a trigger, the wheel will roll down the ramp, perhaps doing damage
Wheels used as turntables are, in general, as easy to detect as pressure plates and related triggers; the crack between the turntable and the rest of the floor is usually visible. Wheels used as rotating shutters are sometimes even more obvious, depending on the thickness of the wheel or any wall covering it. Other wheels are generally hidden behind walls, ceilings and floors, so they aren't readily visible; they will, however, make a noise as they turn.
Wheels can sometimes be jammed by wedging an object between the wheel and another surface, but if the force rotating the wheel is strong, the wedge may simply be smashed or ground up after only a short delay. If the wheel has an axle that is exposed to access and can be damaged, the wheel can be prevented from spinning. Otherwise, adventurers should concentrate on disabling the trigger that causes the wheel to turn or the trigger activated by the turning wheel, rather than the wheel itself. Or, of course, avoid the trap entirely.