Here it is: C E G B D F A ( C E G etc.)
That's it. Memorize it. It's very simple yet it contains all of the chords used in music. It's also the foundation of every arpeggio and scale that you'll come across. It also contains every other chord progression that isn't covered by the circle of fifths. If fact there are only three movements in music: a second (or seventh), a third (or sixth), or a fifth (or fourth). These can all be chromatic or diatonic.
Chord Chemistry 101
Ok, "How is this every chord known to man?" you may be asking. Well all chords are constructed from thirds. There are chords built on fourths and some with 'added' notes but we'll come to that. Every chord is initially built from thirds and then altered from there. To know what the notes are in any given chord, simply start with that note and go in thirds. Of course you're going to have to take into account the key you're in. For example, if you're in the key of E, the E chord will be E G# B D# F# A C#. That's it. If you want to change any of the notes, change it, then make that part of your chord name (e.g. EMaj7#11 = E G# B D# F# A#). So you start on the root and climb in thirds. In the E example above we're looking at the root, third, fifth, seventh, ninth, eleventh, and thirteenth. They all work this way. Not all chords will have all of these notes in it*, but this is the basic foundation.
*Not all notes need to be in the chord; some are 'more important' than others. For example, you usually include the 3rd and 7th since these really define the chord (i.e. major/minor, dominant 7th/major 7th) and the altered extensions. Some extensions, like the 11th in dominant chords is usually left out; others like the 3rd and 7th mentioned above, may be the only notes played. Remember, these aren't hard and fast rules, and can be changed at any time. These are just guidelines.
A Scale Is Just A Linear Arpeggio
One thing that may be a be a bit of a mind bend (at first) is that a scale is just a linear way of looking at a chord. You will come to see that scales and chords are interchangeable and different ways at looking at the same thing. If you look at the notes in a CMaj7 chord and then you look at the C major scale, you'll see that they are almost identical. Improvisers will look at a scale and see the target notes (i.e. notes of the chord) and passing notes (auxiliary notes not found in the chord). Some music (like bebop) was founded on the idea that you could improvise on the upper extensions of the chord and not on the chord tones themselves. A game changing idea at the time.
So What About Those Fourths?
Even though there are chords built in fourths, and others with a fourth or second added, they're still built from this basic chord chemistry. That is, the basic chord is still a C major or D minor (or whatever) but then instead of voicing the chord in thirds, you voice it in fourths. You still name the chord the conventional way (i.e. according to the method listed above). Therefore a chord built on fourths will still be named according to the traditional way. Other chords, like added and suspended chords work in the same way. In fact, once you know the chemistry behind how these chords are built, you can come up with a ton of varieties of your own. The best thing about this is once you've come up with some great chords, you'll know how to name them properly. Again, just use the circle of thirds to figure out what your chord is called, then name it appropriately.
Advanced Arpeggios
Since the circle of thirds is great for chords, the same holds true for arpeggios. Arpeggios are made up of the thirds that we mentioned but once you get into some extended harmonies and altered chords, those arpeggios can get quite hairy. This is where our circle of thirds comes in again. Instead of trying to play all of the notes of the chord, try building the whole thing in thirds. That is, start with the triad and continue climbing from there. You'll find that you end up playing other triads over top of the original triad. This is where polychords come from. Polychords seem really confusing at first but once you've done this exercise a couple of times, you'll see who effective they are. Once you see that for example playing a D major chord over a C major triad automatically becomes a Maj 13 with a sharp 4, trying to incorporate one of these chords into your playing won't be such a problem. This works on many levels. Just go up the arpeggio and see how many triads pop up. Get to know these. Some players rely on these when it comes to altered and extended harmonies because you end up playing new harmonies based on basic triads that you've been playing for years. Don't forget that when improvising, playing around with these extended triads may bring a whole new level to your playing.
Chord Progressions in Thirds
Remember we talked about the ways that chords move. Aside from the fifth movement which we talked about before, there is the second and third. Once you get used to the sound of roots moving in certain intervals, it becomes a lot easier to discern chord progressions and even single lines. When listening to a chord progression, listen to the roots and try to guess which interval they're moving in. Is it seconds (stepwise)? or is it fifths? If it isn't one of the these, it will be our thirds. Some famous chord progressions move in thirds. Anytime the root moves to it's relative minor, it's a third movement. Anytime you hear the famous rock I to bIII, it's a third movement.
E to G is used in millions of rock and blues songs.
So is the E to C (down an third) movement.
Any I to vi or iii is a third movement.
A C#m G Bm is a famous pop progression.
Just to Start
As you can see from the examples, we've just got started on thirds and third movements in chords. The same goes for the chord theory mentioned above. Memorize this circle just like you've memorized the circle of fifths. You'll see these coming up again and again in many things you do. When you have them on the tip of your tongue, it becomes easy to rifle off chord tones, progressions and arpeggios without much thought at all. And that's what we want; we want it to all become automatic.