Fish

FIRST READ THIS
Yes, you can eat fresh raw fish, the Japanese have been doing it for thousands of years (sashimi), but you should only eat fresh raw fish that does not contain parasites. If you are not sure about a specific piece of fish, don't eat it.
To be absolutely safe:
#1 The safest (and most expensive) thing is to eat sashimi in a traditional Japanese restaurant that is also frequented by Japanese customers.
#2 Fresh raw tuna (that has NOT been in the freezer) from a reliable fish-shopkeeper and hatchery-salmon is also safe.

Parasites
Americans in general are quite frantic about raw food, and American sites therefore will tell you that sweet-water fish has to be deep-frozen before consumption. In the USA the FDA in it's infinite wisdom has decided that the almost negligible risk of absorbing parasites should be totally eliminated. Fish that is intended to be consumed in its raw form, has to be deep-frozen first, by law, while freezing does not kill nematodes. Luckily, the FDA has no jurisdiction over the retail operation in general; "the serving of sushi does not fall under their purview". Also see the FDA on seafood
Strangly, the FDA does not mind that the risk of absorbing mutagenic HCA from cooked fish is 100%; cooked fish always contains mutagenic HCA

In fact, absorbing parasites from fish that can cause ill effects, can easily be prevented. Simply stay away from the internal organs, and consume fresh raw red tuna, or farm raised salmon instead of wild salmon.

In the main there are three kinds of parasites to look out for in raw fish: flukes (trematodes), nematodes (roundworms) and tapeworms (cestodes).

Flukes are too big to remain unnoticed. They also are extremely rare.

Nematodes look like big, but short human hair (25-150 mm long, 2 mm in diameter). They lie perpendicular to the fishes' muscle striations (the pattern of striae in the flesh) and have a white translucent sheen. Any merchant - who wants to make sure his customers will not get ill - can detect them using ultrasound.
In particular wild salmon may contain roundworms, but farm raised salmon hardly ever does. There also have been case reports of roundworms from raw Yellowfin tuna causing ill effects in humans. Furtunately, nematodes cannot survive in humans, and only may cause temporary ill effects, such as bloating, cramping and diarrhea.

Tapeworm is the only type of worm that can survive in humans, but their intake can be easily prevented. Tapeworms are found in the internal organs (especially the intestines) and body cavities of the fish. You can avoid ingesting them by only eating the flesh of the fish, staying away from all organs. Tuna does not contain tapeworms.
Fortunately, tapeworms can be easily eliminated with medicines.

The risk of absorbing parasites that can cause ill effects is extremely small; less than 40 US citizens get ill each year by consuming fish containing parasites (in general due to an immune deficiency or due to having consumed some digestive part of the fish). In comparison: every year thousands of US citizens are bitten by snakes.

Of all fish, consuming raw red tuna is safest. Farm raised salmon is much safer than wild salmon. Consuming raw fish other than tuna, you just need to make sure not to consume any digestive organ of the fish, that you check the flesh of the fish, and that your immune system is working properly, so that your body is perfectly able to prevent any possible parasytic infection.

Relying on Japanese tradition and experience, one knows many fish can perfectly be consumed raw. To the Japanese, only serving fish of the best quality and utmost freshness is a matter of honor and ages of tradition. For a list of Japanese Restaurants outside Japan, check this site: http://www.sushi.infogate.de/

Whole Fish
It has to be a whole fish for you to be able to judge its freshness. The slime-layer must be intact. The gills should be moist and bright red (except for mackerel, whose gills are brown). The scales must be both intact and shiny, and firmly attached to the body. The cut edges must have a fresh scent and be moist. If you lightly jab your finger into the meat, it should bounce back. Fresh fish have convex eyes that aren't bloody, but bright white - with shiny black pupils.
And fresh fish does not smell.

Whether or not the fish shop employees tell the truth, you can tell if a fish has been in the freezer because the scales are more open, and fish that has been in the freezer tastes 'watery' and smells strange - not like fish. Herring is never raw because it's not allowed; herring has to be deep frozen for 24 hours to kill possible herring-worms.

The fish with the most fat is the best fish to be consumed raw. Red tuna, therefore, is much better eaten raw than white tuna. Salmon is also a perfect raw fish for consumption. If you want to eat raw mackerel, be sure it's very fresh (sashimi) because you might have an allergic reaction to not-so-fresh mackerel due to its originated amines.
Oysters contain too little fat, too much copper, and far too much zinc (up to 160 mg / 100 g). Zinc and copper are added to cattle's feed to enhance growth and to make their skin shine. Eating oysters can make your skin shine, too, but it can also cause inflammations and severe allergic reactions.

or without frames: