Cancel

Cancels in DMC4 is mostly situational other DT than Vergil and Lady who have a lot of usage in combat.

Nero Uses DT to to cancel any move except for Snatch and Buster, no matter the situation. He can also use Exceed Charge to make quick Aerial Snatch or Taunt cancel for quick DT-Gauge build.
Dante most of his uses are similar to DMC3 until Gilga is obtained.
Vergil uses moves like Rapid Slash to make JJC execution more reliable.
Lady generally uses her shotgun cancel with ground shoot > air shoot to maximize DPS against bosses. She also carry over the charge to the weapon she'd selected, barring handgun/shotgun to kalina ann- that only works one way
Trish uses pandora > lunar phase to skips some sections

Doing multiple Rapid Slash in DT enables you to not only move faster but also skip certain fight triggers like Alto Angelo intro in 9.

General carryover charge method is to release shoot, then switch weapon closely after. Add in a jump if necessary.

Jump Canceling

JC is part of the upgrade shop and it costs heavy proud soul to obtain.

This is mostly important on Dante so, he can recover from moves like Real Impact quickly to make most of his room clears smooth.
JC PF262: Jealousy in DT is a strong tool to un-cloack Mephisto & Faust instantly.
Shotgun Rave has a time-saving potential against Echidna and Angelos.

DT Cancel allows Nero to cancel the recovery off the move, get some free i-frames, or recover from getting hit.

DT Cancel usage entirely depends on the situation so, players use it whenever they think think it's worth it.
It's a free get out of jail card and usually lifesaver against fights like Agnus and Dante.
Buster and Snatch does not cancel the recovery but, it's worth to DT during situation like credo's spear counter or Guard Breaking Sanctus to avoid the transform animation. iFrames

iFrames example against Agnus spinning blade.