Prodigy Math is a free web-based math game that sets up math problems inside a fantasy world. It's popular, but pushes paid memberships to children (or family members with credit cards). While it drills math skills, it doesn't actually teach the skills it tests, nor adapt to learners' levels as effectively as it could.
License: Attribution 4.0 International (CC BY 4.0) (2020)
2024 Update: see Prodigy's current privacy policy; know that Prodigy has expanded to include a Prodigy English game in addition to Prodigy Math.