There seems to be a sore lack of information out there on fish shadows in Animal Crossing, so I did this little blog matching up each fish with its shadow. Unfortunately, all this applies to Wild World only as it is the only AC game I invested enough time in to consider myself "pro".

Fish shadows come in exactly 8 sizes. They're ordered below from smallest to largest (except skinny).

Tiny
Mostly not valuable. Consistent in the sea are seahorse which are worth catching.
bitterling, pale chub, goldfish, popeyed goldfish, killifish, crawfish, frog, freshwater goby, loach, pond smelt, guppy, angelfish, sea butterfly, seahorse, clownfish, can

Small
Not valuable. Commonly produce horse mackerel and crucian carp, both of which are worth little. As such, smalls can often be skipped or scared off.
crucian carp, dace, bluegill, yellow perch, sweetfish, piranha, jellyfish, zebra turkeyfish, puffer fish, horse mackerel, squid, boot

Tweener
Best catch is the barred knifejaw.
koi, catfish, barbel steed, black bass, cherry salmon, barred knifejaw, octopus, football fish

Medium
Red snappers are a decent source of money all year 'round.
carp, char, rainbow trout, red snapper, dab, olive flounder

Large
In rivers, always worth catching. In the sea, they are best ignored or scared away. Except if it's raining...
giant snakehead, salmon, arowana, dorado, sea bass, coelacanth, tire

X-Large
Always worth catching. These guys are very fat and long.
stringfish, king salmon, gar, arapaima, tuna, blue marlin

Finned
Always worth catching. Very distinctive fin poking above sea water.
ocean sunfish, hammerhead shark, shark

Skinny
Slender, unique shape. 100% chance to be an eel, worth 2000 each. A decent catch.
eel

Notes:
- Often the tweener and medium can be confused. Likewise, the medium and large are often confused.
- Each fish species has exactly ONE type of shadow.