As Wordsworth's powers waned, Coleridge trapped in opium induced binges that clamped his poetic powers, and the younger Romantics all dying young in the 1820s, Tennyson emerged to lead the popular imagination into the Victorian age (she succeeded to the throne in 1837). Earlier poems such as "The Lady of Shalott", "Mariana", and "The Lotos-Eaters" exploited the renewed interest in the Gothic, Medieval, and classical themes and stories, while enclosed within highly regular, almost predictable rhythms and verse.
For my money, Tennyson's best work is "Ulysses" and "In Memoriam". Both make strides in poetic form and theme that transcend the period. Ulysses is a stirring peaen to past struggles and the motif of refusing to succumb to adversity. It's ripe for performance and is written in blank verse, similar to a Shakespearean style. However, Tennyson makes the extraordinary choice to compose it almost as an epilogue to The Odyssey, with Ulysses/Odysseus musing upon his life in Ithaca long after his 20 year struggle to return home from the Trojan War. Rather than the "happy ending" of contentment, Ulysses considers that it is mightier and nobler to continue moving, to struggle once again, to fight against old age even as it were. It's some of Tennyson's strongest material, and at 70 lines, is a must read for all poetic scholars and enthusiasts.
"In Memoriam" is a more complex and lengthier epic project. It's a dirge or requiem in verse, with an abba rhyme scheme that shows much more diversity of rhythm and rhyme than other poems of his. The poem struggles with the young loss of his best friend and attempts to reconcile that aching sense of loss in verse. How does one overcome grief when everything reminds you of that person? When you can still feel their presence, their touch, the void left by their loss in everything you do? How does one reconcile that irrational and tragic loss with providence and faith in a higher power? Ultimately, how does one truly say goodbye? How does acceptance gracefully descend on the mourner? It's a lengthier poem that can be read in a few hours but it is well worth the patience of the reader (in the mindset for a more somber poem of course) and is amongst the more profound poems in the English language.
Modern readers will sometimes find Tennyson more iconic of his time than transcendent of it, but I would argue that "Ulysses" and "In Memoriam" truly do transcend it. The other poems are rewarding, but don't expect innovation as much in those works, for a Poet Laureate who reflected a time that treasured order, structure, moralism, and relative normality to the changes in the physical world increasingly dominated by technological change. For a true poetry collector however, it's mandatory stuff with gems dotted throughout the works.