The best replacement for microsoft project is primavera.

The best alternatives to microsoft project are rated as following:
★★★★★  primavera
★★★  basecamp
★★  planningforce
★★  suretrak
★★  projectlibre
★★  wrike
★★  quickbase
★  open workbench
★  trello
★  microsoft excel
★  openproj
★  p6
★  primavera project planner
★  omniplan
★  ganttproject
★  microsoft project server
★  smartsheet
★  project server
★  open project
  open plan
  microsoft visio
  fasttrack
  microsoft office project

Your alternative for microsoft project is not listed? Suggest!
Speaking about microsoft project, one probably shouldn't forget about s curve.

Other search terms related to microsoft project and their ratings are:
★★★★★ s curve
★★★ gantt chart
★ agile
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Google Trends

Scale is based on the average worldwide traffic of microsoft project in all years. Click on graph for more.
microsoft project
primavera
basecamp