How to serve supremely fresh crab? When it's at its best, just eating it directly out of the shell is the way to go (see How to Pick Crab for tips). Or, add a bit more richness by serving bowls of melted butter for people to dip their bites of crab into. To keep things cool and to add more flavor, try Aïoli, a French garlic-infused mayonnaise.
For something less classic, try these Buttery Garlic Crab Bruschetta.
I find Crab Rangoon a great way to use frozen or canned crab, and perhaps a bit of a waste with fresh crab, but if the creamy fried goodness call to you, I will certainly understand. A fresher take, however, are these Crab Avocado Cocktails.