The best replacement for teamcity is hudson.

The best alternatives to teamcity are rated as following:
★★★★★  hudson
★★★★★  bamboo
★★★★  jenkins
★★★★  tfs
★★★★  cruisecontrol
★★  travis
★★  cruisecontrol.net
★★  tfs 2013
★  tfs build
★  buildmaster
★  finalbuilder
★  tfs 2012
  team foundation server
  cruisecontrol net
  ccnet

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

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



Google Trends

Scale is based on the average worldwide traffic of teamcity in all years. Click on graph for more.
teamcity
hudson
bamboo