There are a couple of important aspects to this issue, following up on the two previous responses. As both mentioned, filtration and current are two very different things, though they are connected if the filter is the source of both. It also depends upon the fish and plants, if any.
"Clean" water and "clear" water are not the same thing. The water in an aquarium can be crystal clear but be anything but clean, and vice versa. In a planted aquarium, introduced filtration [i.e., by filter equipment] can be harmful to the plants dependng upon what is involved, and so too can excessive currents. The bioload from the fish may require more filtration, and most aquarists agree that an aquarium with larger fish requires more in the way of filtration than one with shoaling characins, barbs, etc. In an aquarium with few or no plants, mechanical and chemical filtration serves a purpose, depending upon the fish load and size.
In a planted aquarium filtration is the job of the plants, and they do it much better than any filter. In a planted aquarium, the sole purpose of the filter (if one is even used) is to move the water column gently through the tank and through the filter where particulate matter is removed (mechanical filtration). There is no need for chemical filtration in a planted aquarium; using carbon and other media is considered to be detrimental to the plants, since it removes some of the nutrients the plants require. Biological filtration is also completely unnecessary in a planted aquarim, since the plants remove the ammonia/ammonium (and there is evidence that plants may also use nitrite) and what is left is easily handled by the bacteria that colonize every surface in the aquarium, and these will far outnumber the bacteria in the filters.
With respect to current, this should be determined by the type of fish species. Some prefer currents; some South American plecos and catfish come from fast-flowing creeks and are probably in better health when provided with a current in which to swim and graze. But other fish occur in quiet streams and ponds and swamps, and any current beyond the minimum to achieve the afore-mentioned movement through the filter is contrary to the fish's requirements. One of the marks of a successful community aquarium is having species of fish that occur in the same type of environment; this can prevent stress which can lead to poor health and disease. As mentioned earlier, strong currents are also not desireable in a planted aquarium.
Aside from the above issues, in an aquarium with fish and no plants, can excessive filtration be harmful to the fish? I don't know, frankly. But, it costs money to acquire and operate filters, and it may be money wasted if there is no purpose served. In nature water is constantly moving past the fish, even in all but the smallest of isolated ponds and swamps, and even then there is water exchange via evaporation and rain. No filter can compete, since no filter can exchange water; a filter can only remove certain properties from the water, but it is the same water, so there may well be no positive benefit to the fish from filtration beyond the minimum necessary to maintain the fish's optimum health.