Thank you for these answers. My robin sightings decreased over the first few weeks since I wrote this, however they're back in full force now. This made me curious enough to do further research, and I happened upon two fact sheets about American Robins, whose scientific name is Turdis Migratorius, meaning Migrating Thrush.
I've extrapolated data from a series published by Learner.org entitled Journey North, and will be referring to and quoting sections of this and this.
As indicated by the thorough sources referenced in @fileunderwater's excellent answer, it's clear that not all robins migrate, and among those that do, there are a number of variables, many of which are not fully understood. Robins are considered nomadic, meaning they travel in many different directions, and, unlike other species, they don't necessarily come and go from the same location, further complicating the study of migration.
In general, food supply is the robin's most important consideration, and weather controls the availability of that food, so a complex combination of the two appears to be the main migration trigger.
Migrators rely heavily on earthworms, caterpillars and other insects for the bulk of their diet.
In the fall, they fly south because the ground freezes, locking them out from their favorite food, earthworms, and because winter weather makes it impossible to find juicy caterpillars and other insect food.
The same theory applies in their motivation to return from the south. Soils in the south can get so warm and dry that worms retreat deeper into their burrows during hot, dry spells, making them harder for robins to find.
Robins are easily overheated, so they become stressed and restless when the southern temperatures remain high for an extended period of time.
The south to north migrators are programmed to follow something called a 37-degree isotope. They move ahead of warm fronts, the intention being to settle down where the temperature averages 37 degrees or more. That weather pattern also brings spring rains, causing the ground thaw that triggers the end of earthworm hibernation.
The male robin migrates first. He bulks up by eating more than usual to sustain him through the arduous journey, which is why the first robins we see are generally chubby! (The male also has a much darker head than the female.) As @fileunderwater pointed out, in some areas robins have begun to arrive significantly earlier, while the ground is still frozen, so that extra preparation helps them survive for a time by eating berries and insects found in trees. If all else fails, some will re-join a flock and fly to a warmer area for a few days or weeks, which supports my recent observation.
Upon arrival, the male's job is to stake out a territory conducive to good breeding conditions. Once he finds an area that has a good feeding source, a safe place for breeding, and the right materials for the female to create a nest, he spends most of his time in a nearby tree singing. It's a unique sound rarely used at any other time, and it lets other males in the area know to stay away.
A few weeks later, the female arrives. Her trigger seems to be related to ideal nesting conditions.
She has no urgent need to return early, since there is nothing important for her to do until there is a good mud supply for building her nest. As a matter of fact, if she builds too early, hard frosts at night can weaken her nest. And if she runs out of food too soon before the nesting season, it can make it hard for her body to produce eggs. So she waits until conditions are more favorable and she can continue to get a reliable winter diet as long as necessary.
A few other fun facts about migration:
Robins migrate mostly at night.
They fly at speeds of 30-36 mph, traveling between 100 and 200 miles per day.
To keep from getting lost, they figure out their location on the planet in much the way sailors on the high seas once did--using the angle of the sun in relation to the time of day. If blown off course, they fly to where the sun will be at the proper angle.
Flock sizes during migration vary greatly. Although groups of 10-50 are the most commonly seen, they'll fly in groups as few as three or four, and I (the author of one of these articles) once counted 60,000 robins flying along Lake Superior in just 5 hours!
For various reasons, many robins don't survive migration. Scientists estimate that only 25% of fledglings born in the summer survive until November, and even many experienced adults die during migration.