Here's a personal favourite of mine: Gruntz (1999)
A Puzzle-Stratedgy game, with a storyline, custom levels and free-play. (Has multi-player, but I've never gotten it to work).
This was actually my childhood game, which I found on Real-Arcade as a demo, and eventually convinced my parents to purchase the full copy.
This game was developed by Monolith Productions, the same people who made Shadow of Mordor. But Gruntz was quickly forgotten after its release.
Amazingly, however, the official forum for this game is still up: http://gooroosgruntz.proboards.com/
The thing that amazes me even more is that it's being managed and paid for by an Eighty-Three year old.
As I mentioned before, this does have its own storyline in single-player, but eventually you'll run out of these levels to play. Luckily, there's a handful of people whom have made custom levels for you to play on your own. I have no idea if the editor for these levels is still available. These custom levels are also found in the forum mentioned above.
Either way, I found this game to be an enjoyable experience. One I loved as a kid. I would love for someone to look this over, I think this game has potential to be a Game Dungeon episode.
I DO have a copy of this game, however it's not patched and doesn't include the cutscenes.