Dash-dancing is useful for all characters to some extent, but more useful to those who
1) have a fast initial dash animation
2) have a long initial dash duration
3) have good aerials (dash-dancing lets you launch any aerial in either direction almost instantly)
4) have a good up-smash (can JC into it from dash dance)
5) have a good dash grab
6) have useful pivoted attacks (Marth)
7) have a decent over-B or up-B (can use from dash dance)
Fox meets 1, 2, 3, 4, and 5. Captain Falcon meets 1, 2, 3, 5, and 7. Marth meets 1, 2, 3, 5, 6, and 7. Pichu meets 1, 2, and 4. Etc. Requirements 1 and 2 also determine if the character has a decent foxtrot, which is useful as an extension of dash dancing.
Dash dance is useful for Ice Climbers because you can desynch from it.