Urochordates and neural crest
The neural crest is an example of a profound evolutionary innovation in vertebrates. It seems to be something simple—it's a population of cells that are 'left over' at the closure of the neural tube, and that wander out into the other tissues of the body—but it has been co-opted in numerous ways to provide major vertebrate features. You wouldn't have much of a face without the neural crest, for instance; this plastic population of migrating cells get recruited to build much of what lies below your eye sockets, along with some radical reorganization of branchial arches. These cells also form the insulating myelin sheaths of your peripheral nerves, and most visibly, form all of the pigmentation in your skin. Having neural crest in the embryo, obscure as it is to most people, is considered to be one of the hallmarks of being a vertebrate, and without it you'd be pale, slow, and very, very ugly.
One particularly pressing question, then, is where the neural crest came from (and no, divine prestidigitation or alien tweaking aren't under consideration, at least not until someone comes up with actual evidence for such designer intervention.) Where should we look? In lineages that branched off of the chordate line before the evolution of vertebrate neural crest. One such lineage is the urochordata.
Urochordates are very cool creatures. As adults, they are sessile blobs called sea squirts; they settle down and squat in one place, sucking in sea water, filtering out small organisms for a meal, and squirting it back out again. Some adults are even colonial, forming clusters of filter-feeding lumps in which individuals are often ambiguous. They reproduce by producing free-swimming larvae, though, that have classic chordate characteristics: a tail with a notochord, a dorsal spinal cord, segmented clumps of muscle, and pharyngeal feeding structures. The larva wiggles away from its parents, finds a new spot to settle down in, and throws away most of its brain, its notochord, etc., and becomes a blob itself (most human teenagers, I think, see this as a parable for their parents life, I'm sure.)

Ecteinascidia turbinata. a, A colony showing gravid zooids (arrow). b, The giant Ecteinascidia tadpole (above) compared to a small Styela clava tadpole (below). c, A diagram of the Ecteinascidia tadpole, showing the CNS (blue) with melanized sensory cells (black), branchial siphon (bs), atrial siphon (as), endostyle (e), heart (h), perforated pharynx (p), digestive tract (d), and tail (t). d, Orange pigment cells distributed throughout the body wall and concentrated in the siphon primordia of an Ecteinascidia tadpole. Scalebars: a, 1cm; b-d, 800µm.
Urochordates are not considered to have anything like a true neural crest, a population of plastic, pluripotent migratory cells that adopt multiple fates in the organism. A paper by Jeffery et al., though, has found that they do possess migratory cells that arise near the neural tube, and that develop into one of the canonical neural crest types, pigment cells. It's a kind of proto-neural crest.
They did this in the simplest way possible: they labeled groups of cells near the nervous system with a fluorescent dye, and then watched to see if any moved away, and where they ended up. They observed cells migrating away from the nervous system to take up positions near the prospective siphons, where they differentiated into orange pigment cells. They also probed these cells for markers we find in vertebrate neural crest, Zic zinc finger transcription factors and the cell surface glycoprotein HNK-1, and presto, they are expressing neural-crest-like molecules in addition to acting like neural crest.
It seems like such a trivial thing, that these animals have a few cells that wander off to make a few orange spots on their skin, but it's these small, simple innovations that provided the foundation for the acquisition of further potential roles. We can put together a solid model for how these features evolved based on the developmental evidence.
First, the neural tube/CNS attained the capacity to generate migratory pigment cells, possibly as a means to protect a sessile ascidian-like chordate ancestor from the harmful effects of sunlight in shallow marine habitats. These migratory pigment-generating cells may have been lost secondarily in amphioxus, which live buried in marine sediment and lack body pigmentation. Alternatively, it is conceivable that urochordates are the true sister group of vertebrates and that the migratory cells evolved in their common ancestor after the divergence of amphioxus from the chordate lineage. Later in chordate evolution, probably at or near the base of the vertebrate radiation, the primitive migratory cells gained additional functions and/or were joined by other cell types to generate the multiple derivatives characteristic of the neural crest.
Jeffery WR, Strickler AG, Yamamoto Y (2004) Migratory neural crest-like cells form body pigmentation in a urochordate embryo. Nature 431:696-699.


Very cool work!
"The larva wiggles away from its parents, finds a new spot to settle down in, and throws away most of its brain, its notochord, etc., and becomes a blob itself (most human teenagers, I think, see this as a parable for their parents life, I’m sure.)"
In Consciousness Explained, Daniel Dennett mentions tunicate metamorphosis--especially the eating-one's-brain and becoming sedentary--and adds, "It's sort of like getting tenure."