Mr. Nutz Hoppin' Mad uses every trick in the book! It uses dual playfield mode with multiple levels of parallax in the background playfield with palette changes every few scanlines to make the mountains/background objects different colours, as well as extra levels of parallax in the city level that I don't know where they come from (are they sprites or something?). It changes the palette for water areas and switches on the audio filter when you're under the water. It has those 3D third-person tunnel levels from State of the Art, and massive end of level bosses that zoom in and out to become twice as big as your screen. On top of all that, it's super fast, colourful, a joy to play, and has a huge map full of heaps of levels.
Brian the Lion also pushes the Amiga hardware quite a bit. It stays in single playfield mode, but still manages parallax with a repeated sprite layer in the background so it can use more colours in the foreground. It uses scanline-palette changes, translucent water, massive rotating platforms, and that lovely map that zooms into the screen.
Fightin' Spirit, while not using any special tricks, manages to push the OCS chipset to its limits in some ways too. It has the largest BOBs of any fighting game on the Amiga, which are actually larger than the Street Fighter II, King of Fighters and Street Fighter Alpha sprites. The whole game runs in 64 colours (Extra-Half-Bright) but makes better use of the palette than any other EHB game (they don't use the second bank of colours JUST for shadows, but for everything). It also has that awesome rock song at the start with the lyrics (although I have no idea what they're saying).