Step 1: Cut sides away from pit
Using a sharp paring knife, start just off the centerline and cut parallel to the seed along the long axis of the fruit. If you contact the seed, just curve away a bit to follow the contours of the pit. You'll leave more flesh on the pit, but it's not going anywhere. Once you get a feel for the seed sizes in your mangos of choice, this process will get even tidier. You should see the white pit showing in the center piece when you're finished.
Cut both sides off of the pit in this fashion, and set them aside.
Step 2: Remove skin from center piece
Now that you've skinned the center, go ahead and eat it. This is the best part of the mango, and it's your treat for cutting up the mango for your lazy friends or family. Use your teeth to scrape all of the mangoey goodness off of the pit, then remember to floss. Mango pits are fantastic, but also the best impetus to floss this side of corn on the cob.
Step 3: Score the sides
Make a series of parallel cuts, taking care not to cut through the skin. Poking through the skin results in an untidy mango, dripping mango juice, and sometimes blood. Cut the lines as close as you like, so long as you make at least two of them.
Now, spin the mango 90 degrees and repeat the process.
Step 4: Invert
Note that if you've made less than two cuts in either direction, the mango won't have enough flexibility to invert neatly. The more cuts, the easier it will flip and the better it will look. Here I've gone for a middle-of-the-road approach; sometimes I like to have lots of tiny mango spikes.
Step 5: Serve
This is especially good brunch/buffet food, as it's reasonably mess-free and doesn't require utensils. Just hold the mango and bite off the spikes. Alternatively, slice the spikes off at the base for perfectly-sized mango chunks!