well there are a lot of point and click adventures like monkey island on amiga,one of the most obscure one which i liked a lot because it's simply weird is gobliins 2 and i don't mean just weird... i mean WEIRD
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one game that sure left an impression was moonstone though probably it was more because of it's gorish setting than anything else... i think it even predate mortal kombat so for once the gore was added just because
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ah cannon fodder is a classic,it's a somewhat unique game you drive a platoon of 4 soldiers from a top down perspective and shoot at stuff with your left button,it's kinda like playing a RTS only imagine you have 4 units and they are VERY frail so being quick with your finger at shooting is a lot more important than strategy
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another game i liked a lot was superfrog,it's kinda like sonic and although there a lot of cheap death,i still soldiered on,i blame the music
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oh crap can't believe i was forgetting this,this is like the best amiga game ever,seriously if you have to pick one,pick this
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do you like shooters? this one is pretty weird,the hero gets turned into a bee and then you get on to fight a variety of insects,one of the level is inside a sewer and the first boss is a really gross dead rat with worm's bursting out of his body

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to be fair it's kinda hard recomending amiga game because a lot of them simply have gotten better versions as DOS games (like syndicate)