My google news alert for "squid" frequently pops up recipes and restaurant reviews, most of which I dismiss out of hand. But a critical mass of alerts mentioning squid ink pasta, risotto, and other dishes finally drove me to a more thorough investigation.

I found a great article on called Sleuthing Squid Ink. This guy really did his homework: he made five different squid ink dishes from Italy, Spain, the Philippines, and Japan. Even more admirably, he talked with my pal Stephalopod, an awesome lady who researches squid ink, in order to figure out the chemical underpinnings of squid ink flavor, which is apparently "briny with a rich seafood essence" in addition to having an "earthiness like old, wet leaves." Mmmmm, briny leaves! I can't imagine anything more delicious!
Before I got started, however, I noticed my squid ink wasn’t squid ink. It was from cuttlefish—the squid's larger, thick-fleshed cousin.
Science correction! Some cuttlefishes may be larger than some squids, but on average, squids are the heavyweight champions. Giant cuttlefish are a couple of feet long; giant squid are much bigger than a person. And I'm not really sure what "thick-fleshed" refers to. The mantle tissue of big Humboldt squid is a couple of inches thick--a solid calamari steak if there ever was one.
Concerned that I might be cheating if I used cuttlefish ink instead of true squid ink, I found this info from Marcella Hazan's Essentials of Classic Italian Cooking that put me at ease: "To the Italian palate, the harsh, pungent ink is the least desirable part of the squid. As Venetian cooks have shown, it's only the mellow, velvety, warm-tasting ink of cuttlefish—seppie—that is suitable for pasta sauce, risotto, and other black dishes." I did a bit more shopping around, and it appeared that most of the "squid ink" on the market is actually cuttlefish ink.
Whoa. I never would have guessed there would be a gustatory difference between cuttlefish and squid ink. Maybe I should look in this paper that Steph pointed out to the author, which is where
I found my answer for squid ink’s kickass seasoning effect: High concentrations of glutamic acid, also (improperly) known as glutamates. Like MSG, fish sauce, soy sauce, or Parmigiano-Reggiano, squid ink adds to food that alluring fifth taste: umami. Deliciousness.
Actually, umami taste receptors don't detect just glutamic acid, although that's their most famous stimulus. They can detect most amino acids, of which glutamic acid is only one.

The authors of the aforementioned paper were looking for all kinds of amino acids in animal inks, because amino acids are thought to be one of the ways that ink works as a defense mechanism. This works (it is theorized) because predators (like us) are specially tuned to detect amino acids (for nutrition) so inking prey (like sea hares or squid) can throw us into a confusion by overloading our amino-acid-detecting senses. This can happen by one of two methods:
Sensory disruption results from secretions massively stimulating the predator’s chemosensory systems, preventing normal function, which leads to confusion and cessation of attack by the predator. Phagomimicry results from secretions stimulating the predator’s sensory pathways involved in feeding, thus causing the predator to attend to the secretions as if they were food and thus affording the sea hare an opportunity to escape.
So, what makes cuttlefish ink "mellow and warm" while squid ink is "harsh and pungent"? Is it differing quantities of glutamic acid, all amino acids, or something else entirely? Here is a subset of the paper's massive Table 1 (units are micromolar):

Glutamic acid
 135 66
Total Free Amino Acids
 2,542 1,675 455 2,114 14,381
Ammonium 4,595 310 216 423 1,307

Yes, cuttlefish have more glutamic acid than any of the three squid species studied--but much, much less than the octopus! The same relationship holds true for total amino acid concentration: cuttlefish have more than squids, but octopuses have WAY WAY MORE than cuttles. Does that mean that octopus ink would be as much more delicious than cuttlefish ink as cuttlefish ink is than squid ink?

Wait, hang on, check out those ammonium concentrations. Here is where cuttlefish are clearly the winners. Could ammonium possibly be warm and mellow? It's difficult to countenance. In most articles about giant squid, like this one, ammonia is mentioned as the offensive substance that renders them inedible . . .

From the cephalopod's perspective, it doesn't matter. If their ink smells yummy, the predators are distracted and they can get away. If their ink smells foul, the predators are deterred and they can get away.