Fin rot
Fishes' fins turn whitish and die back. Fin rot often follows damage or injury. It can also be caused by poor water quality.
Remedy: First, fix the water and remove any fin-nipping fish. Change some water (25% is good) and add 1 tsp/gallon salt to promote healing. If bad water quality or an aggressive tankmate was the problem, that should be adequate. Healing will begin within a couple of days.
If it worsens, decide first whether it's fungal or bacterial. Fungal finrot looks like clumps of cotton on the fins and usually follows injury. It is commonly seen in African cichlids or fish that have injured themselves against decorations. Bacterial finrot is whitish, but not cottony (unless it's columnaris), and can be contagious. The fish then need to be removed from the tank and medicated.
Fungus: For fish large enough to handle, catch the fish, and dab malachite green directly on the fungus with a Q-tip. This is extremely effective. Repeat treatments may be necessary.
For small fish, a commercial fungicide such as Maroxy may work. For severe infestations, try a bath in methylene blue (enough so you can barely see the fish) until the fungus turns blue or for 20 min. If you add methylene blue directly to a tank, you will kill plants and trash your biological filter.
Bacterial: Antibiotic treatment in a quarantine tank. This is stressful for the fish, and doesn't always work, so be sure of what you are doing before you attempt it. If the fish is still eating, the best bet is an antibiotic food. Tetra makes one that works well -- just buy the one for bacterial diseases and follow the directions on the can.
If the fish is not eating, a bath treatment is necessary. A combination of Kaynamycin and Furanace usually works, especially for Columnaris. Again, treat in a separate tank and aerate heavily