Fish have many of the same brain and nervous system aspects as mammals, and have even been sucessfully trained by ambitious individuals, so it is very likely that they have the capacity to be bored. However, there are not particularly toys pre-made for fish, so the best thing you could do to spice up thier life would be to provide behavioral enrichment, as many zoos and aquariums do. Enrichment comes in many forms, but generally involves exposing the animal to social and behavioral stimulation similar to what they would experience in the wild, as well as providing living conditions that mimic thier habitat. Further entertainment can be provided by changing the surroundings moderately (ie. moving plants and decorations about, adding and removing decor, etc.), providing live prey, or purchasing a suitable companion fish.
I firmly believe that fish in dull, barren, and exposed settings can indeed become nuerotic, and exhibit depressed and repetitive behavior; just watch a lone fish from a social species in a bland tank and you'll see what I mean.