Hex nuts are used to fasten parts together such as a hex bolt or screw.  They come in a variety of sizes, grades, and coatings.  The thread types for hex nuts are either course or fine.    

Jam nuts have half the height of standard hex nuts.  They can be used where there is not enough space for a standard hex nut.  They also can be placed with a regular nut to hold it into place and not allow the regular nut to back off.  Used most in machinery and equipment.

Left hand nuts tighten when turned counterclockwise so they do not loosen during motion in that direction.  You can find them applied in machinery or equipment use.

Slotted hex nuts, or castle nuts, have a hex body and slots cut near the top like that of a medieval castle.  These are used in conjunction with other fasteners like a cotter pin.  The cotter pin gets placed through the slots of the castle nut then slides through the hole of the fastener like a hex bolt with drilled hole.  These are not recommended for high vibration applications because of the shearing potential of the pin.  The total height of the slotted hex nut includes the slotted portion.