Below are various quotes from people on various sides of the Accessibility vs Difficulty Debate, a number of them taken from the sources cited in the bibliography separately posted. I’ve tried to represent common threads of the debate, as well as the sometimes heated and personal tone of the discussion.
Disclaimer: These are snippets, no more. In almost every case, the expanded views of the authors are more nuanced.

Jorie Graham

“…the difficulty of poetry, even for its most sympathetic readers, is a real one. Or rather it is both real and imagined. Much of it dissipates as one opens up to the experience of poetry.”

Stephen Dunn

“When people praise a poem that I can’t understand I always think they’re lying.”

Adam Kirsch

“There is a distinction, however, between the difficulty of obscurity and the difficulty of complexity. The latter emerges naturally from any attempt to capture a new feeling or idea for poetry. But with Graham, as with so many self-consciously modernist poets, the difficulty seems to fall into the first category. Her poems are obscure because they seem unfinished, because they reside in the privacy of the poet’s mind and not in the public realm where poet and reader discuss things in common. As long as Graham asks the reader to fill in her blanks and solve for her x’s, she has not realized poetry’s greatest and most enduring possibilities.”

August Kleinzahler

“Are we not yet adult enough as a culture to acknowledge that the arts are not for everyone, and that bad art is worse than no art at all; and that good or bad, art’s exclusive function is to entertain, not to improve or nourish or console, simply entertain.”

Billy Collins

“I am bored by poems that are transparent from beginning to end, but I am quick to put down poems whose opening lines make me feel I have walked in on the middle of a Swedish movie being run backward with no subtitles.”

Brian Henry

“But because Collins obviously has a stake in the legitimacy of the accessible poem and the speciousness of the difficult poem, he must attack the authors of difficult poems, not just the poems themselves. The fact is, difficult poems often seek a deeper connection with their readers than most accessible poems (especially Collins’s) do. By virtue of the work—active reading—a difficult poem can require, the reader can join the poet, temporarily, in the act of the creation and interpretation of meaning. The difficult poem can enlist the reader as much as it can shut out the reader, but Collins does not acknowledge that site of possibility because it is not in his best interest to do so.”

Mark Halliday

“’Will Clover or his admirers respond to my review? Probably not, though they blog constantly. Why should they respond? I’m on the other team (the lyrical and/or narrative mainstreamy team). We grant tenure to our players, they grant tenure to theirs; mostly we avoid shootouts. Ignoring is incredibly easy in our literary culture. Someone should write a big essay on literary ignoring. (But most readers wouldn’t pay attention to it!) We just ignore what irritates us, and everybody can keep on harvesting the fruits of polymorphous academia (while we all go on detesting Republicans and mega-corporations, of course); we don’t have to respond when baloney wins awards, because there are so many other awards—and what really matters? What matters, if the twenty-first century is bound for hell and we’re all lost in the supermarket?’”

Matthew Zapruder

“[S]urely the most frequent accusation leveled against contemporary poetry is its difficulty or inaccessibility. It is accused of speaking only to itself, or becoming an irrelevant and elitist art form with a dwindling audience. … [U]ntil finally we cease to trust the power of poetry. We ‘accept the limitations’ of the medium. … We become anecdotal. We want to entertain. We believe we should ‘communicate’.
…
What is the purpose of literary criticism? Among other things, to guide the reader past his or her resistance. Most art, subtly or aggressively, resists the familiar. Poetry in particular suffers from this resistance, because poets take the material that we depend on to operate in and make sense of the world (language), and bend it to other, often seemingly obscure, purposes.”

Bill Knott (in response to Zapruder)

“‘What is the purpose of literary criticism? Among other things, to guide the reader past his or her resistance.’ —hoo boy, what arrogance—the “reader” doesn’t need a guide; most readers are intelligent enough to find the poets they need to read without being led by the nose by critics—Hillman’s and Armantrout’s readers for example, all 800 of them, and Mary Oliver’s readers, all 80 thousand of them—this kind of arrogant condescending Zapruderism is what drives so many potential readers away from poetry: fortunately there are counteractive patrons of poetry, Garrison Keillor for one example, who bring accessible poetry to a wider audience—Zapruder is an elitest promoting elitest poetry, but who knows, if he works at it he might increase its audience to 801.”

Ted Kooser

“We’ve become accustomed to being confronted by poems that confuse, baffle, embarrass, and initimate us, and for a lot of people, reading poetry is a dreadful experience, that is, an experience full of dread. As poets we need to think about breaking down reader resistance…”

Reginald Shepherd

“Many years ago, I sat in on a class of Ted Kooser’s in which he asserted that a reader wants to be led by the hand through a poem, that readers have no patience with being baffled, no tolerance for mystery. I had to interject that I hated to be led by the hand through a poem. I’d rather that the poet assume that I can make my own way through a poem, though I do prefer that there at least be pathways, even if they’re not paved and lit. I don’t object to being baffled, though I also don’t want to remain in bafflement indefinitely. Just as mystery can be part of a person’s allure, so mystery in poetry can be a lure: Yeats calls this ‘the fascination of what’s difficult.’”

Steve Kowit

“[Reginald] Shepherd … rejects any poetry that makes so much as a grain of sense, for such poetry, according to him, refuses to ‘honor language,’ something that is done, apparently, by treating it as an end in itself. Shepherd wants a poetry of ‘strangeness and opacity,’ one that exhibits a ‘resistance to communication….

Let us, by all means, have a poetry of the most incandescent verbal pyrotechnics, of the most restlessly experimental and original design. Let us have poems that astonish the reader at every turn. Let our poets attend to making it new with nearly as much fervor as they attend to making it true. But on those occasions when we fail to communicate, let us no longer imagine we have succeeded at something larger and grander. Let us not blame our failures on the intellectual poverty of our readers, or on their inability to register complex ambiguities, or on their irritable reaching after fact…. Let us no longer be gulled into imagining that rhetorical sophistication and verbal panache in the absence of genuine, communicated perception can create a poetry that is genuinely complex, textured, multilayered, exploratory, intuitive and profoundly insightful, a poetry worth careful study. They create, rather, poems that are hardly worth reading through once. ”