The best replacement for vnc is remote desktop.

The best alternatives to vnc are rated as following:
★★★★★  remote desktop
★★★★★  rdp
★★★  vpn
★★  logmein
★★  teamviewer
★★  tightvnc
★  nx
★  pcanywhere
★  ssh
★  nomachine
★  rdc
★  radmin
★  real vnc
★  rdp security
★  spice
★  ultra vnc
★  x11
  citrix
  chrome remote desktop
  terminal services
  gotomypc
  tight vnc
  dameware
  x2go
  team viewer
  remote desktop connection
  rdesktop
  ultravnc
  udp
  apple remote desktop
  freenx
  mstsc
  x11 forwarding
  xming
  jaadu remote desktop
  netmeeting
  terminal server
  microsoft remote desktop

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

Other search terms related to vnc and their ratings are:
★★★★★ ssh
★★ file transfer
kde
You have in mind a companion for vnc and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of vnc in all years. Click on graph for more.
vnc
remote desktop
rdp