Games I know of on Android:

• Ganz Schön Clever — Digital adaptation of a board game. It's like bingo except you roll dice and there's actual skill involved.
• Knotwords — Crosswords but instead of word clues, each region of the board indicates what letters appear there.
• Threes — 2048 was a ripoff of 1024, and 1024 was a ripoff of Threes. Threes is the OG.
• Sagrada — Digital adaptation of a board game. Build a stained glass window by rolling dice and placing them on your board in the right pattern.
• Simon Tatham's Puzzles — Big compilation of various puzzle types.
• Handshakes (by Pet Pumpkin) — "Solo co-op" sokoban puzzle where you try to get two guys to shake hands.
• inbento — Assemble lunch boxes by sliding tiles around to match the reference picture.