Colonization happens in most strategy games but not always under that name.

• Colonization (1994) was the original by Sid Meier.
• Colonization too was a free imitation, sadly abandoned in about 2004. Its material remains available. See https://sourceforge.net/projects/coltoo/ and some notes on the FreeCol forums.
• FreeCol is an open source free-to-play imitation, under constant improvement since its launch in 2003.
• Civilization IV: Colonization, a remake of the 1994 game (not requiring Civilization IV), was developed by Firaxis Games and published by 2K Games in September 2008.