Q:

Why do these four chords make hit songs?

So music has a popular set of chords that appears very often: I IV V vi. It's the primary triads + 6th chord, which is also the relative minor. Of all the chords I find that these are the most popular and appear in the most songs, especially the ones that top the charts.
I was watching this great busker which made me think about it. Most buskers play I IV V vi songs again and again because it is what gets the audience most excited. Here's the chords to a few of those songs. Ed Sheeran also mentioned this in an interview, "You name any song and I'll play them in 4 chords". Same was shown by axis of awesome.
But I was just wondering what it is about these chords that people are so drawn to them that they appear again and again? They seem to make hit songs.

A:

I would disagree in that first, if 1 4 5 6 are the rule, then there are lots of very effective and widely used exceptions to the rule. Secondly, I think all of the first six diatonic chords are equally important and used. The vii dim is rarely used.
It all comes down to diatonic harmonic function. Classical music theorists might disagree but basically the I, iii and vi are tonic chords, the ii and IV are subdominant and the V (and vii dim) are dominant. We are all used to hearing and like chord progressions that make use of the relationships and movements between these types of chords. 

A:

Chords, of course, are made of notes - and one way of looking at why notes have strong harmonic relationships between them is to look at the frequency ratios between them. Note pairs with simple frequency ratios have a strong harmonic relationship because some of the harmonics will coincide (assuming the timbre we're using has an ideal harmonic series). 
The simplest ratios are 1:2, 1:4... and so on. These are octave relationships; we tend to hear these as 'the same note, but higher'.
The next simplest ratio is 2:3. That coincides with the musical interval of a fifth. If we imagine that our root note is 100Hz and our fifth 150Hz, we can see that the root will have harmonics at 100, 200, 300, 400, 500, 600, 700, 800, 900.... Hz, while the fifh will have harmonics at 150, 300, 450, 600, 750, 900... Hz. The harmonics in bold are in common to both notes.
And the next simplest after that is 3:4. That coincides with the musical interval of a fourth. 
So any chord rooted on the fourth (IV) or fifth (IV) has a root that has a very strong relationship with the tonic. 
We can also use these ratios to see why a major chord in itself sounds so strong. As well as the fifth (2:3) we have a major third (4:5) - also a very simple ratio.
So major chords based on I, IV and V are themselves based on simple ratios, and have roots that have relationships based on simple ratios. The upshot of this is that you will find that some of the harmonics present in chord V or IV are also present in the I chord. (Because chords are made of notes, and notes are made of harmonics, we can see chords as the superset of the constituent notes' harmonics.)
Looking at the IV chord itself - not only it is a major chord that contains the tonic note, but the third of the tonic chord acts as a leading note to its root. And looking at the V chord - its third acts as a leading note to the tonic. So motions between these chords are aided by the presence of these leading notes.
Taken as a set, the chords I, IV, and V contain all notes in the major scale. This is why it's often claimed that you could go better than Ed Sheeran claims in his quote, and use just those three chords to harmonise any major scale melody.
As to why the vi is popular - Richard has given some great reasons in his answer to Why is the vi chord so popular?. I would add that for whatever reason, minor chords are often associated with sadness, so adding the vi chord to your palette gives you an easy option for creating some emotional movement. As well as having two notes in common with the tonic chord, the vi also has two notes in common with the IV.
So, there are many reasons why those chords have strong relationships with the tonic, and can work well with each other. 

A:

I'll state what I notice about your theory. First off, those are the primary chords of the Major scale, except for that relative minor, and we have a preference for the sound of those chords. The predominant reason we use those chords for composing our music is because we like the sound of them when they are played together. That's the same reason our melodies use the same notes together, they have been time tested and they sound good together when we use them together. Some folks believe it's magic, and some believe it's inspiration from the cosmos, I don't know, maybe it is. However, I found in my experience that things become a hit because a lot of people like it, and it seems a lot of people like the sound of those chords together,  which inspires songwriters to use them a lot. Simple as that.

