I looked over this long thread and noted that no one pointed out why they three chords are used to accompany a song.

Let's take the key of C, which, as we know, has no sharps or flats. So a song in that key, usually, will have only the notes

C D E F G A B C

And the I, IV & V chords used to accompany a song in C are:

C F G (or G7)

So what are the notes (the "do, mi, sol") in each chord?

C = C E G
F = F A C
G = G B D
G7 = G B D F

Now, how many notes in the scale are NOT covered? None. And how many notes NOT in the scale are included? None.

That's why the I, IV, & V(7) chords work so well.

If you wanted to use the major chords for the notes in the scale, you'd add accidentals (sharps or flats) that are outside the scale:

C = C E G
D = D F# A
E = E F# G#
F = F A C
G = G B D
A = A C# E
B = B D# F#

As you notice, there are sharps (or corresponding flats) that aren't in the C scale, so it's an unusual song that includes those notes ("unusual" means maybe 5%-10% of songs, but some genres have a larger percentage). So it's less common to use those other chords.

Now, when you need those other chords, which ones are the most common? Well, the II chord (D in the key of C, for example) is common, but mostly as a leading tone. The II leads to the V (D --> G) regularly. That is the V chord of the V chord, if you look at it. Some even call the II chord the "double dominant" since the V chord is the dominant.

An aside - the I chord gives you the tone, so it's the tonic chord. The V chord is the dominant chord, pushing you toward the tonic (which is why it dominates). The IV chord is the sub-dominant (under the dominant, of course). And the II is the double dominant.

Back to the chords. We see that C --> D --> G is a common pattern. And D is the V of G which is the V of C.

What's the V of D? Why, A is. So a pattern you hear now and then is C --> A --> D --> G --> C. This circular pattern of V chords is sometimes called "the circle of fifths," which shares the name of the key patterns mentioned above (that clock face). By the way, it's normal to use the 7th version of the chords except the I (so you get the "Don't Let Your Deal Go Down" pattern of C/A7/D7/G7/C, for example).

So you can use the circle of fifths to determine key signatures (number of sharps or flats), the I, IV, & V chords (from any place on the circle, the IV is one step anti-clockwise, and the V chord is one step clockwise), and which chords to play when the I, IV & V aren't the only ones.

Learn that circle; it's good for you, it's the "Mandala of Western Music" as I saw it in a chart on the web. It's Gospel!

Bob