The best replacement for bbpress is buddypress.

The best alternatives to bbpress are rated as following:
★★★★★  buddypress
★★★★  phpbb
★★★★  simple press
★★★  vanilla
★★  vbulletin
★★  mybb
★  mingle
★  xenforo
★  vanilla forums
★  punbb
  wp-forum
  mingle forum
  simple:press
  buddy press

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

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



Google Trends

Scale is based on the average worldwide traffic of bbpress in all years. Click on graph for more.
bbpress
buddypress
phpbb