The best replacement for activesync is imap.

The best alternatives to activesync are rated as following:
★★★★★  imap
★★★★  bes
★★  mdm
★★  ews
★★  exchange
★★  owa
★★  mapi
★★  syncml
★  mobileiron
★  outlook anywhere
★  windows mobile device center
★  pop3
★  caldav
★  good technology
★  hotsync
★  wmdc
★  airwatch
★  bes 10
  goodlink
  oma
  touchdown
  windows device center
  pop3\/imap
  intellisync
  webdav
  windows mobile device centre
  blackberry enterprise server
  pop3 imap
  exchange 2007
  exchange web services
  wireless sync

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

Other search terms related to activesync and their ratings are:
★★★★★ owa
★★★★ exchange 2003
★★★★ outlook 2010
★ device
★ blackberry 10
★ exchange server
★ bes
You have in mind a companion for activesync and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of activesync in all years. Click on graph for more.
activesync
imap
bes