Inky caps are easy to recognize once they mature, because rotting like a regular mushroom is too slow a process for these species. The gills will actually deliquesce and turn to ink from the outside in, until only a stem remains. You can actually fill a fountain pen with the "ink" and write with it. Many of these species are edible, but of course it is recommended to eat them when they are young before they have started to turn to ink. This process can take place anywhere from a few hours to a few days into the life of the mushroom, which means that they need to be eaten quickly after being found. However, 30 seconds or so in a microwave is said to kill the enzyme that causes them to turn to ink allowing you to store them for longer. This may work for Coprinus comatus, but the others are too small and will just turn into a soggy mess.
Inky caps are recognized by dry caps, gills that are often free or almost so and very crowded together, black spores, and often an umbrella shaped cap that is taller than it is wide. A universal veil often leaves material on the cap, which is typically not hygrophanous. They are all saprophytic. Only Coprinus comatus has a partial veil. It leaves a ring on the stem. Most have caps that are strongly striate. The odd character of turning into ink appears to have evolved twice, as the famous Shaggy Mane is related to Agaricus and the rest of them are related to Psathyrella. In these, the cap cuticles are cellular, meaning that the caps can break easily in any directions (as demonstrated on the Psathyrella page). The entire fruit bodies are often very fragile like Psathyrella as well.
Not every inky cap turns to ink, a few do not, but can often still be recognized by their fragile, striate cap and black spores.
Coprinus comatus - "Shaggy Mane". Remarkably, this mushroom is related to Agaricus. The rest are related to Psathyrella.
Coprinus comatus - our largest inky cap with large scaly cap, much taller than it is wide. The gills are extremely close together like the pages in a book and will turn black from the spores, and then liquify into ink. Caps up to 10cm high. Stem hollow with a thread running through it (to separate it from the others after it's dissolved).
Coprinopsis - white to greyish caps often with shaggy or scaly velar material on the cap (or if not, will be especially large (>5cm) or especially minuscule (<1cm), and are usually striate. Found on the ground, wood, or sometimes dung.
One species, C. atramentaria, contains Coprine, the active ingredient in Antabuse. If you eat this mushroom either a few days before or after consuming alcohol, you will get sick, as Coprine will interfere with the body's ability to process the toxins in the alcohol. Another group, the C. lagopus grp, is so short lived you have to be in the right place at the right time to see it during the only few hours a year it will fruit. Fortunately it is incredibly common, and you will find it at least in its inky state all the time.
C. lagopus grp - very short lived, always copious velar material on the cap. Grey. Ground or burnt ground. <5cm.
C. friesii - purple grey, in grass, does not deliquesce as much as C. lagopus. Velar material on the cap. Small, cap <1.5cm tall.
Coprinellus/Parasola - usually brownish, sometimes grey. Strongly striate. Caps usually between 1-5cm and may have granular particles, but not shaggy or scaly velar material like Coprinopsis. Found on the ground, wood, or sometimes dung (see Coprinopsis for tiny dung species).
C. micaceus - glistening mica-like particles on a yellow-brown cap <4cm high (larger than the others). The particles wash off easily. Browner in age than Parasola and C. impatiens.
C. domesticus - larger particles, orange felty mat sometimes in the substrate.
C. flococulosus - felty patches on the cap, in wood chips.
C. disseminatus - grows in large clusters, small (~1cm). Particles on cap like C. micaceus, but does not turn to ink.
Parasola plicatilis/lactea - separated by their bald caps with the finest pleats almost to the centre and not turning to ink. Free gills with a collar. In grass (P. lactea also found in disturbed soil), unlike the C. impatiens group. Brown turning grey except in the centre. Cap <2cm high.