Hagfish are wonderful, beautiful, interesting animals. They are particularly attractive to evolutionary biologists because they have some very suggestive features that look primitive: they have no jaws, and they have no pectoral girdle or paired pectoral fins. They have very poorly developed eyes, no epiphysis, and only one semicircular canal; lampreys, while also lacking jaws, at least have good eyes and two semicircular canals. How hagfish fit into the evolutionary tree is still an open question, however.
There is a strong temptation to see hagfish as representing an earlier grade of evolution than the lamprey, regarding them as a sister group to the vertebrates, with a tree like this:

If the hagfish is regarded as a sister group of
the vertebrates, Conel’s description of an “epithelial crest”
appears to be an intermediate state of the fully evolved crest,
which delaminates to produce migrating crest cells, as seen in
vertebrate embryos including lamprey embryos.
The primitive features of the hagfish represent a contemporary retention of the ancestral state. One of the key pieces of evidence for this version is the development of the neural crest, illustrated in green on the right. The neural crest is a highly plastic population of migratory cells that arise at the time of the closure of the neural tube; in vertebrates, these arise by delamination, or separation of the cells, from a dorsal epithelium. Earlier reports of neural crest in hagfish suggested that they arose in that animal as epithelial pockets, a very different approach, and that the evolution of the neural crest was from an initial state of a set-aside epithelial tissue.
I described some other work on the evolution of vertebrate eyes in which the authors make an argument this sister state of the hagfish is valid, and that therefore the time of divergence of the hagfish represents a lower bound on the period when eyes evolved. Hagfish don’t have image-forming eyes at all; lampreys have good image-forming eyes; if the tree diagram above is correct, we can narrow down the period of eye evolution to the time between the branching of the hagfish line and the divergence between lampreys and the gnathostomes, or jawed vertebrates. Cool.
There’s an alternative picture, though. Hagfish could be degenerate forms: the jawless fish, lampreys and hagfish, form a monophyletic group, and the hagfish secondarily lost their eyes. In this model, they really don’t tell us much at all about the ancestral state, because their morphological simplifications are not primitive at all — they’re more recently evolved specializations.
If this is the case, than the tree should be redrawn like this, to illustrate cyclostome monophyly.

Monophyly of the Cyclostomata is consistent with the
actual development of the hagfish crest and with the recent
observation of presumed “neural-crest-like cells” in ascidian
embryos.
This is an active debate right now. As I mentioned, one side is testing hypotheses by looking at the details of cellular organization and molecular pathways—if the hagfish has molecular relics of a more complex ancestral visual system, for instance, that would reinforce the idea of cyclostome monophyly. I’ve also reported that hagfish eggs and embryos have finally been successfully raised in the lab, and the results so far are that they don’t have an unusual mode of neural crest formation at all — previous interpretations otherwise were the result of fixation artifacts, and hagfish seem to make neural crest by delamination, just like everyone else. There is also a growing body of molecular information that’s tying hagfish and lampreys closer together.
Personally, I think the argument for cyclostome monophyly is growing stronger, while those who think hagfish are a more primitive sister group seem to be fighting a rising tide of evidence. Still, this is how scientific debates are settled: by testing hypotheses and gathering evidence. We follow where the data leads.
OK, that’s all very rarefied and academic, but here’s another reason hagfish are just plain interesting: they’re weird, and they do many things in such a different way than we vertebrates with our faces and our jaws are used to imaging them. Here, for example are a few frames from a video sequence showing how an alien eats a piece of meat.

Successive video images of the moment of feeding. The fish protrudes a pair
of plate-like “horny teeth” (tp) ventrally to capture the bait (cod meat). Also note the tentacle surrounding the dorsal “nostril” (no) and the
ventral “mouth” (mo).
Spectacular!
Kuratani S, Ota KG (2008) Hagfish (Cyclostomata,
Vertebrata): searching for the ancestral developmental plan of vertebrates. BioEssays 30:167-172.