This is a little unusual in the list, because it's a game I only discovered very recently. Sure, I was aware of its existence but I hadn't played it and never thought twice about it. I ended up trying it by default when playing around with a BBC emulator recently. I mean, when you've got a BBC emulator what do you play? Repton, Elite... and Exile.
After smacking myself 'upside the head' for a while for being ignorant of this amazing game all these years, I settled down to play it intensely and ended up favouring the Amiga version for its clarity of visuals (I spent an awfully long time stuck at the very beginning of the BBC version because I couldn't tell what anything was supposed to be). However, it remains a classic in all guises, and a genuinely amazing feat of programming and execution on the BBC.
Marrying the gravity gameplay to a sprawling, puzzle-based adventure game, Exile casts the player as an astronaut sent to a remote world to stop an insane genius from unleashing his deadly experiments on the galaxy and Earth. Arriving without equipment and low on power, you have to search for items and weapons to aid you, while fighting off the creations of the exiled madman.
The behaviour of the astronaut with regard to gravity, weather and physical interaction with other objects is so satisfying. The delicate controls beautifully responsive. It's an immense pleasure to just move around in the game, but there's a job to do. Exile can be a real head-scratcher, with some serious lateral thinking required, but it's also very accommodating to the player. You can't die in the game - you just return to your last 'remembered' position when you take too much damage (you can hold one position in memory at a time and teleport to it at will - a vital component of several puzzles).
Exile is a game that not only provides a compelling challenge and an attractive gameworld, but also has a particularly attractive feel to it. Something unique to videogames.