Mines-Perfect by Christian Czepluch (excuse his English) — effectively demonstrates why more than one mouse button isn't necessary. Also guarantees that games generated should require no guessing. Also has multiple shapes: 6-neighbors, 7-neighbors, 8-neighbors(square-tiling), 8-neighbors(parquet-tiling), 12-neighbors, 14-neighbors, and 26-neighbors. Also has an auto-solver based on rule complexity! (so you can practice learning a new rule by having it solve all lower-complexity rules, and only leaving the situations that you're just now learning to solve) Also allows maximum board size of 44x78, which is kind of epic.
Novel Mines by NovelGames (the original NON-FLASH one (no, the downloadable-but-still-flash version doesn't count either)) — lots of different shapes (3-neighbors, 4-neighbors, 6-neighbors, 8-neighbors, and 12-neighbors). Historical versions are: