The experience of eating a fresh-caught crab is completely different than eating one that's been hanging out in a tank for weeks, FattyDumplin pointed out in a recent Chowhound discussion about blue crabs. The meat from a freshly caught crab is "firmer, sweeter and much tastier, in large part because I think the crab in a tank literally starts to lose muscle mass due to the inactivity," FattyDumplin says.
If you're lucky enough to get live crabs and want to keep them that way for a few days, you should keep their gills wet so they can get oxygen from the air—don't submerge them in water. Instead, cover the crabs with a lot of wet newspaper and store them in the fridge, porker says. Wet the newspaper again after two or three days. "I've kept lobster, rock crabs, and blue crabs alive for 4-5 days this way," porker says.
Wet seaweed is great in place of newspaper, Veggo says. With the addition of a few small ice packs, crabs stored that way in a hard-walled cooler can even survive airplane travel.