A knowledge of chord progressions will help you communicate and play with other musicians. It is a must for participating in any kind of jam session. Knowing the most commonly used chord progressions and forms allows for greater enjoyment and unity when playing with other musicians.
Most songs use three or more chords though some songs exist that only use two chords. Often musicians will embellish chords by adding or removing notes and to provide further interest may vary the rhythm. One chord "structures" are uncommon but they do exist. For instance, Frere Jacques is a one-chord song because it can be played against a single major chord. The melody "Taps", traditionally used at American military funerals, and which is very evocative, consists only of the notes which comprise the C-major chord (C, E, G). One chord songs are rare on guitar.
The I-IV-V 
The most common chord progression is the I-IV-V. Note that Roman Numerals are used to describe these chord progressions. Many songs use only these three chords. If one views chords as a set of balancing scales with the root note and octave root at opposing ends it will be noted that the IV and V chords are at equal distance respectively to the root and octave root. Take for example the key of C major:
C - D - E - F - G - A - B - C
You will see that the G note (or chord) is a fifth above the root note. The note F is a fifth below the octave. This movement of a fifth is very pleasing to the human ear in its sense of balance and cohesion in relation to the root note. Another way to view chord progressions is that of a journey. In the sense that the root (or tonic) chord is the starting point and the octave root is at the end. All other points (chords) provide interest and variation with the fourth and the fifth chord occupying a special place on the journey due to them being half-way.
Many chord progressions start at the tonic (I), moves away to somewhere else, only to come back to the tonic. You can play this progression with major chords or you can substitute minor chords for the IV or V.
Applying the I-IV-V 
This progression is pretty much the backbone of popular western music. Eddie Cochran, Muddy Waters and Buddy Holly are three artists who have used this progression extensively with great effect. Note that this chord progression uses a V7 chord. A V7 chord is just a V chord with an extra note. It is so common a device that when learning a chord progression many guitarist will play it through a few times using I-IV-V (normal V chord with no extra note) and then will play the chord progression I-IV-V7 a few times before switching back to the normal I-IV-V.
The I-vi-IV-V 
When picked with triplets, this progression is most commonly recognized from rock ballads in the 1980s, but it is widely used in many other styles of music. This progression is commonly referred to as the 50's progression, because it was common to many of the popular songs of the 1950's, notably "Stand by Me". Here's the progression in the key of G major.
The I-V-I-I 
This is a popular progression at the beginning of a much larger line, and can be combined with many other scale degrees.
The ii-V-I 
As its name indicates, the progression is: ii-min7, V7 and Imaj7.
Alternatively you can change the chord type on the II, and alter the voicing of the V. Some examples are:
- ii-m7b5(9) V7alt Imaj7
Applying the ii-V-I 
ii-V-Is can be chained together, creating complex progressions. Here's an example:
C Bm7b5 E7 (I ii V) Am7 Dm7 G7 (I ii V) C (etc...) (I etc..)
An example of complicated progression that can be created this way is the "Coltrane Changes", where the "I" chords move by Major 3rd intervals. Here's a simple example:
Dm7 G7 Cmaj7 (ii V I ) F#m7 B7 Emaj7 (ii V I ) Bbm7 Eb7 Abmaj7 (ii V I ) Dm7 etc... (I etc...)
The way the ii-V-I progression works is first that it moves by 4ths upwards, which very often produces interesting results, and the 7th goes down a half tone below and becomes the following chord's 3rd.
The Minor ii-V-i 
Another commonly used chord progression is the minor ii-V-i. One can derive this from the melodic minor scales shown above, while substituting a IminMaj7 for the IMaj7 chord, or by using three modes from one harmonic minor scale , which produces the following chord progression: