I wish either my father or my mother, or indeed both of them, as they were in duty both equally bound to it, had minded what they were about when they begot me.

Ten times a day has Yorick's ghost the consolation to hear his monumental inscription read over with such a variety of plaintive tones, as denote a general pity and esteem for him;—a foot-way crossing the church-yard close by the side of his grave,—not a passenger goes by without stopping to cast a look upon it,—and sighing as he walks on, Alas, poor Yorick!

Digressions, incontestably, are the sunshine;—they are the life, the soul of reading!—take them out of this book, for instance,—you might as well take the book along with them;—one cold eternal winter would reign in every page of it; restore them to the writer;—he steps forth like a bridegroom,—bids All-hail; brings in variety, and forbids the appetite to fail.
...
All I wish is, that it may be a lesson to the world, "to let people tell their stories their own way."

Never taught it, but always thought it might be fun to do with Northrop Frye's "Archetypes of Literature" essay. It's not technically about the poem, but it could work anyway.

I had them do some group work where they analyzed the changing descriptions of different aspects of the setting: the sea, the sun, the weather, the sea creatures, and the ship. I assigned each group one of these categories, and they had to find the relevant descriptions and explain how they change/shift throughout the poem and what that contributes to the plot. 

 We talk about the ballad, archaic language, the circulation of the Mariner's tale, genre, environmentalism, and we talk a lot about zombies.  In terms of environmentalism, I introduce the Book of Genesis' notion of man's environmental stewardship over nature, and we discuss if this is the rationale behind the poem's message, as stated in the last few stanzas. It isn't as if the Mariner completes his voyage and then surrounds himself with nonhuman animals--he remains anthropocentric. So I ask them: what, then, is the function that animals are put to in the poem? And doesn't this reinforce a particular human/animal hierarchy? Also, I like to push back against the stewardship theory by exploring how ineffable and powerful nature is in the poem, and how impotent man seems to be against it.

The game is done! I've won, I've won!

It ceased; yet still the sails made on A pleasant noise till noon.

Full many shapes, that shadows were, In crimson colors came.

I moved my lips -- the Pilot shrieked and fell down in a fit

I pass, like night, from land to land; I have strange power of speech.

The moment that his face I see, I know the man that must hear me.

I frame discussions of it around the impact of WWI and resistance to both Victorian culture and Victorian narrative conventions. My students have read Wuthering Heights first, so we get some mileage out of comparing Clarissa's choice between Richard and Peter to Cathy's choice between Edgar and Heathcliff (thinking about how this novel explodes the two-suitors marriage plot and figures it retrospectively). We also talk about Septimus in relation to changing paradigms of mental health and illness in the early twentieth century. 

On Septimus and mental health

I talk about how nineteenth-century understandings of nervous disorders like neurasthenia (symptomology we would now associate with depression) totally failed in explaining and treating shell shock. Holmes and Bradshaw are following the "rest cure" approach to Septimus, and obviously, it's exactly what he does not need.  See historian Janet Oppenheim's Shattered Nerves for information on nervous disorder/depression treatments in Victorian/Edwardian England. See also Cathy Caruth's theories of trauma and narration and talk about WWI as the beginning of modern trauma studies. 

On the two-marriage plot:

Jean Kennard's Victims of Convention (there's an article and a book by that name) is an oldie but goodie. She outlines how the traditional female Bildungsroman requires a female protagonist to choose between two suitors who represent different cultural values. In choosing the "right" suitor she accepts his values, but loses her autonomy. Kennard talks about how this limits the kinds of female experiences the traditional novel can tell; obviously, it excludes maternity. Clarissa's story references the two suitors convention but insists that a woman remains fluid, interesting, and complicated after she has "chosen." And then of course there's all the interesting same-sex desire stuff in that book. Sharon Marcus's Between Women is an interesting lens for looking at Clarissa and Sally in their youth.

She would not say of any one in the world now that they were this or were that. She felt very young; at the same time unspeakably aged. She sliced like a knife through everything; at the same time was outside, looking on. She had a perpetual sense, as she watched the taxi cabs, of being out, out, far out to sea and alone; she always had the feeling that it was very, very dangerous to live even one day. Not that she thought herself clever, or much out of the ordinary. How she had got through life on the few twigs of knowledge Fräulein Daniels gave them she could not think. She knew nothing; no language, no history; she scarcely read a book now, except memoirs in bed; and yet to her it was absolutely absorbing; all this; the cabs passing; and she would not say of Peter, she would not say of herself, I am this, I am that… Her only gift was knowing people almost by instinct, she thought, walking on. (200)

I'd second Gretchen's advice, but also point you in the direction of empire and imperialism. London itself is a character in the novel, and it's important to consider the urban space, and in particular the way that space is mostly limited to Westminster. It's the metropolitan center and focused even more on the state apparatus/government. Peter's recent return from India of course feeds right into this reading. Big Ben is the masculine time of governance and empire (and St. Margaret's, always two minutes behind is, at least in Peter's mind, feminine time).

There are many more paintings in this Houses of Parliament Series.