Lateral Thinking

1, 3 & 5 in the chord of E major are the pitch classes E, G♯ & B. If we map out every instance of these on the first 12 frets of the guitar, we see that they divide themselves naturally into our 5 major shapes:1

E
[6]
[4] 2
[2] 5
[5] 7
[3] 9

We can do something similar with the remaining basic open major shapes (G, A, C & D). As you play through these, it should become obvious that they are just different sections of a single repeating pattern (...[6], [4], [2], [5], [3], [6], [4]... as you go up the fretboard

G
[3]
[6] 3
[4] 5
[2] 8
[5] 10

A
[5]
[3] 2
[6] 5
[4] 7
[2] 10

C
[2]
[5] 3
[3] 5
[6] 8
[4] 10

D
[4]
[2] 3
[5] 5
[3] 7
[6] 10

To get familiar with these relationships, practise the following exercises. Feel free to experiment with other voicings, add melodic improvisations within the shapes etc. Also, once you're comfortable with these exercises, adapt them for the remaining major chords.2

E
G
A
C
D

By this stage, you shouldn't have much trouble figuring out how to adapt this material to minor chords, but I'm going to include the shapes anyway just for the sheer hell of it.3

Em
[6]m
[4]m 2
[2]m 5
[5]m 7
[3]m 9

Gm
[3]m
[6]m 3
[4]m 5
[2]m 8
[5]m 10

Am
[5]m
[3]m 2
[6]m 5
[4]m 7
[2]m 10

C
[2]m
[5]m 3
[3]m 5
[6]m 8
[4]m 10

Dm
[4]m
[2]m 3
[5]m 5
[3]m 7
[6]m 10

Notice that we now have two kinds of relationship between our shapes:


In these diagrams I've decided show, except for in the open-position chords, the practical movable shapes rather than the notes on all 6 strings. I think this makes it easier to get to grips (pun intended) with how the shapes fit together- it's not difficult to ‘fill in the blanks’ once that familiarity has been achieved.
I.e. D♭, E♭, F, F♯/G♭, A♭, B♭ and B. Notice that these are all within a semitone of one of the five ‘open’ shapes.
As mentioned elsewhere, the [2]m shape can be awkward to finger - drop either of the root notes if you need to.