The camo cloaks the fellowship got seemed to only approach being magical, they weren't quite I don't think - I suppose some of the stuff for hunters in Cabela's catalog is as good.
In LOTR, magic plays a very important part at times, but it is always in the background. The main characters, the hobbits, are about as non-magical as one can get.
But I don't buy it when some try to say that Tolkien portrays all magic as evil. He doesn't. Only the Ring and similar evil magic is portrayed as intrinsically evil. They're evil not because they're magic, but because their purpose is to dominate and enslave, which intentions would be equally evil if they used a non-magical method.