"Chaucer" to most people means the Canterbury Tales. But should it? Over the years, I think I've taught every Chaucerian work in the canon, except for "A Treatise on the Astrolabe" and "Anelida and Arcite," at least once, and yes, I do include the Melibee in that list. For graduate classes, the syllabus has varied more widely than for the undergrads—even though many grads have not had any undergrad Chaucer, or even any undergrad medieval lit, so there is an argument for giving them a "standard" Chaucer, too.
If there is such a thing as a "typical" undergraduate Chaucer course in my repertory, it tends to include several of the Canterbury Tales plus one of the less famous texts, usually either Troilus and Criseyde or the Book of the Duchess. Lately I've just been doing Canterbury Tales and short lyrics.
My recent trawl through other people's syllabi suggests a fairly even division between CT-only courses and CT-plus-Troilus courses. It has been a few years since I last taught Troilus, and I want to bring it back. In fact, I want to make it the main focus of the class, because I think then I could structure the course in a way similar to the way I structure my Arthurian class, which usually goes much more smoothly than the Chaucer classes: begin with a modern translation of an early source (Latin or OF), and only deal with Middle English after the broad outlines of the plot have been digested. This also allows me to introduce close reading through analyzing different translations of a single Latin sentence, along with a representation of that sentence accompanied with a super-literal translation plus parsing; after that, the whole idea of the close reading goes a little better.
But since people seem to think "Chaucer = Canterbury Tales," I suppose I had better include some of them. Let's put it this way: what tales would you be absolutely shocked to learn that an English major didn't know? Channel your inner old fart, and comment.
Or, if you're not amused by fart jokes (some Chaucerian you are, in that case), which tales "go" best with TC? (Your litel tragedie, does it go? Bet it does, bet it does!)