PS: turns out it is somewhat species dependent:
http://www.mass.gov/eohhs/docs/dph/environmental/foodsafety/...
As with most things in life, it's really a question of risk and trade-offs. Parasites are rare enough in tuna that they are below the risk threshold for most people. Salmon less so, though it depends on where you get it and how much you trust them.
The broad guideline is that deep, open water, fast-moving fish have a lower parasite load than fish who live closer to shore, closer to the bottom, and/or don't move as fast.
Thus, tuna is pretty safe. But you're gonna want to cook an eel or a catfish before you stick it in your mouth.
One of the things I find fascinating about sushi but try not to think about too much, is that the clear implication is that all of the needed-to-be-frozen sushi I have eaten probably did have some parasites in it. I just ate dead parasites, which I admit is better than eating live ones. Safe, but still kind of gross.
There is no standard or regulation that designates fish as "sushi-grade." It's a popular misconception.
I'd rephrase that as being able to spot fully grown parasites easily, but parasites don't always come fully mature.
I don't think that's generally the case. As far as I know, the main salmon parasites that we care about are Anisakis (nematodes) and Diphyllobothrium (tapeworms). The former is much more common than the latter, especially in the US where as far as I know broad tapeworm has only recently been detected in a small fraction of Alaskan salmon.
Anisakis has no terrestrial hosts. Its lifecycle is crustacean -> fish -> aquatic mammal (whales, dolphins, seals) -> repeat.
Humans and other land mammals are the host of Diphyllobothrium, but, again, I don't think that's very common. From what I've read, most of the need to freeze salmon comes from wanting to deal with roundworms.