The best replacement for gotomypc is logmein.

The best alternatives to gotomypc are rated as following:
★★★★★  logmein
★★★  pcanywhere
★★  vpn
★★  remote desktop
★★  webex
★  gotoassist
★  logmein pro
★  vnc
★  gotomeeting
★  teamviewer
★  remote desktop connection
★  splashtop
★  windows remote desktop
  pcnow
  pc anywhere

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Speaking about gotomypc, one probably shouldn't forget about logmein.

Other search terms related to gotomypc and their ratings are:
★★★★★ logmein
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Google Trends

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gotomypc
logmein
pcanywhere