Mike Hall's Reversi
A light and portable Reversi game with animated moves and 4-level difficulties.
Pros & Cons:
Weighing in at 127 KB only, Mike Hall's Reversi is a good choice with a nice and clean user interface. It has a built-in engine with 4 levels of strength, undo/redo and animate moves. Saving games is not included.
Another small program is Edge Reversi with a download size of 338 KB. Simple user interface with no animation effects. Undo/redo moves and saving games are included. You can limit computer's moves by time or search depth.
Both these programs are portable: after downloading, just unzip to any folder you choose, click the executable, and start a game.
Mike Hall's Reversi was reviewed by Gizmos Freeware on based on version 2.0.