The best replacement for quake 3 is quake live.

The best alternatives to quake 3 are rated as following:
★★★★★  quake live
★★★★★  quake 4
★★★★★  unreal tournament
★★  counter strike
★★  ut99
★  unreal tournament 2004
★  openarena
★  ut2004
  quake 2
  unreal 2004

Your alternative for quake 3 is not listed? Suggest!
Speaking about quake 3, one probably shouldn't forget about urban terror.

Other search terms related to quake 3 and their ratings are:
★★★★★ urban terror
You have in mind a companion for quake 3 and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of quake 3 in all years. Click on graph for more.
quake 3
quake live
quake 4