Major seventh (Ma7) or sixth (6) chords can be substituted for Major chords. A C (5433) chord can often be replaced by a CMa7 (5432) or (4433) or by a C6 (2433). Likewise, a D (2225) chord can often be replaced by a DMa7 (2224) or a D6 (2222*). This will not always sound great, but try it and see where it works.
A dominant seventh, as ubulele said above, has the greatest number of options for chord substitution. A G7 (4535) can be replaced by a G9 (4555*)[This is not a complete G9 chord, since it does not contain a root, but having only 4 strings, we must sometimes make compromises] or a G7b5 (4534) . . .
*The G9 can also serve as a Dm6 and the D6 can also serve as a Bm7.
Since these are all closed chords, they can be moved up and down the board with the appropriate name changes.
Another handy chord for swing/jazz sounds is the diminished or diminished seventh chord which can be named after any note in the chord (2323) goes by the name A, D#, F# or C dim.
Some handy turn-arounds (or intros) are 2 beat each of C, A7, Dm7, G7 or C, C#dim, Dm7, G7 or C, Em7/Ebm7, Dm7, G7 (one beat each for Em7 and Ebm7). Notice that they all begin on C, the tonic (or CMa7 or C6) and end on G7, the dominant (or a suitable substitution for the dominant).