Some thoughts on guitar chords. There's a standard lexicon at the bottom if you're just looking for basic chords that you'd like to know. The General section is for some more experimental ideas.
See also thoughts on harmony.
Allan Holdsworth says that he finds ..3210 to be an ugly and dissonant Maj7 chord, and that he prefers ..1014, with the root on the top E string. This is the same as .1004 and 1003, which are quite easy to play. A nice bonus about this is that playing .1004 as a I chord means that it's easier to use an E-tonic iii chord and its variations.
Stretching to 0..444 or 0..144 has a nice sound. The problem with 0.110 is that it's a very deep, sonorous chord, which is not always what you want from a Maj7 inversion. Often when you're playing a strong Maj7 like a IMaj7 or a IVMaj7 you want a brighter sound. You get that with 0..144 especially, with the lowest-string tonic. On the A-string, .0212 is fine. As a variation on Maj7, ..1031 {1,3,7,2} i.e. Maj7,9, is nice. Sometimes just playing the standard D-string ..0222 Maj7 is a nice variation of the 0.110 pattern and in the same sort of area that you'd start out in.
Speaking of sonorous Maj7 chords, 02.12 is a particularly sonorous way of doing a Maj6. Note that when you play that as a I chord, you can dip down to 02.13 as a simple VII7 chord and it sounds pretty great even though you have a pretty weird and chromatic {7,TT,b3,6} relative to the I there.
Dm9b5 idea, used in Django's Diminushing: 1..103
2000 / .2001 / ..2011 are a great shape.
..0111, a Dø7 shape, fits into the A9 shape, .10111
2..310 is an excellent variation on 1.120
The b5add6,9 chords, 1200 / .1201 / ..0100 clearly fit into the E7 shape, 020100, which means that the IVb5add6,9 chord substitutes with V7, giving a nice ambiguity between IV and V.
Movement from I to IV can be achieved using 0..112 which has a b6 passing tone, and from IV to I you can use iv7 of course, which can be played as either .0212 or, often better, .2023. This also has a b6 passing tone in it, relative to I.
Map compact chord notation to diagrams:
These chords are taken from standard chord introductions, and then arranged according to the taxonomy that Joe Pass uses: E- and A-tonic chords grouped together into three kinds by underlying triad plus seventh, with diminished grouped under dominant seventh chords.