Someone in this thread mentioned JetSet Willy. That did actually see a release on the Amiga, as I have it in my collection.
One of the enjoyable things about the original Spectrum version was that the game was a flip-screen affair, so you were always keen to see what delights the next room had to offer. This was a scroller, and much of the charm of the original was lost.
The music was also very poor, and the collision detection iffy. Still, I did like the nice images that were displayed when you visited different parts of the house (while the game loaded those parts of the map in).
There have been a few mentions of Sonic on here. Back in the day I remember reading that Neo approached Ocean with an Amiga version of Sonic, but were told to go away and use the engine for something else, which is why we got Mr. Nutz, which looks a lot like a Sonic game.
Whether there's any truth in that, I don't know. Sounds plausible, though.