The best replacement for jump is hop.

The best alternatives to jump are rated as following:
★★★★★  hop
★★★  leap
★★  dive
★★  logmein
★★  branch
★★  jiggle
★★  junk drive
★★  next
★★  imagine
★  applecare
★  shuffle
★  long jump
★  seed cannon
★  broad jump
★  bunny
★  crawl
★  vertical jump
★  splashtop
  att next
  jumps
  jump around
  fly
  standing jump
  was she pushed
  nanta
  catapult
  country jump
  boxer shuffle
  high jump
  triple jump
  teleport

Your alternative for jump is not listed? Suggest!
Speaking about jump, one probably shouldn't forget about parachute.

Other search terms related to jump and their ratings are:
★★★★★ parachute
★★ running start
You have in mind a companion for jump and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of jump in all years. Click on graph for more.
jump
hop
leap