What is the "truss rod" on a guitar? Do truss rods vary for an acoustic, electric, or classical guitar?
A neck is not unlike a bow (like bow-and-arrow). Like a bow-string, guitar strings bend the neck and make it arc. Obviously, you don't want the neck to bend as much as a bow, or else you'd never be able to play it. But you actually want the neck to have a little bend in it, or else the strings will lie flat on the frets and won't be able to vibrate freely. The amount of bend your neck has is called its relief.
If the strings don't exert too much tension, then they'll only bend the neck a little bit, and everything will be fine. This is the case with classical and nylon-string guitars. But steel strings exert much much more tension than nylon strings, and so they will actually bend the neck considerably—so much so that the guitar would become unplayable. That's where the truss rod comes in. It's a steel rod imbedded inside the neck. It counteracts some of the tension of the strings and keeps the neck from bending too much.
The great thing about most truss rods that the amount of tension they absorb is adjustable, so that you can actually adjust how much relief your neck has by increasing or decreasing the tension on the truss rod. This allows for very precise adjustments to the action of the guitar, making it very easy to play.
A truss rod stabilizes the neck of the guitar. Depending on the type of guitar or banjo, they are made from different materials and are located in different places on the instrument. See here for more info:
To answer the unanswered part of the question, yes, they vary from guitar to guitar. Almost every steel-strung instrument has a truss rod. But some classical guitars, with the lower string tension associated with nylon strings, have no truss rod at all.
In essence the truss rod is a means of applying a force to the instrument's neck to counteract the forces exerted by the tension of tuned strings. Steel strung instruments in particular have very high tension when tuned and can easily distort the neck material if it is not reinforced.