Body
This is the largest part of the guitar and the most obvious. On Classical, Acoustic and some Electric guitars this is hollow, to allow the sound to be created. Many guitar specifications will mention a 'solid top' - this is the top of the body you can see in the picture. Different woods will offer different sounds and qualities. Solid Sitka Spruce is very popular but you'll also see Mahogany, Nato and Bubinga.
Cheaper guitars often use a laminate for the top. These offer lower sound quality but are much cheaper to produce which is normally reflected in their price.
Saddle/Bridge
The Saddle and Bridge are where the strings fix to the body. They help to transmit the sound and vibration of the strings into the body to create the sound. Strings are either knotted (on a classical guitar) or pegged (as above).
Fretboard
This is where your fingers do the work - the frets are the spaces between the metal strips which move the strings up in semitones. Different combinations of frets produce different chords and scales.
The fretboard also takes alot of punishment as it's the most used part of the guitar. I recommend using Lemon Oil when changing the strings. This helps to clean the fretboard and keep the wood supple. Fretboards are traditionally Maple or Rosewood.
Nut
This is where the strings leave the next before attaching to the tuning pegs on the headstock. A properly adjusted nut is important (as well as the bridge) as this will determine the action of the strings (how far above the fretboard they are). Too close and the strings will buzz, too far away and the guitar will be harder to play.
Tuners
These are used to alter the tuning of the individual strings. Standard tuning is EADGBE, but artists like Crosby, Stills and Nash used EBEEBE on songs like Suite: Judy Blue Eyes as seen in the video below, and other artists regularly use Drop D - DADGBE and heavy metal music regularly uses other non-standard tunings.