Actually, Goldfish DO have long-term memory.
The story is apochryphal, as with so many anti-science anti-biology arguments...
http://www.theage.com.au/articles/2008/02/18/1203190696599.html
"We are told that a goldfish has a memory span of less than three seconds and that no matter how small its tank is, it will always discover new places and objects," Rory said.
"I wanted to challenge this theory as I believe it is a myth intended to make us feel less guilty about keeping fish in small tanks."
Rory's experiment involved teaching a small group of fish to swim to a beacon by establishing a memory connection between the beacon and food.
Over a period of three weeks, he placed a beacon in the water at feeding time each day, waited 30 seconds and then sprinkled fish food around the beacon.
The time taken for the fish to swim to the beacon reduced dramatically, from more than one minute for the first few feeds to less than five seconds by the end of the three weeks.
Read more, it gets even better...