Don't use code (unless computer code is part of the poem). Don't use blockquote (unless you quote a poem).
white space / line breaks: pre or br
You may use the pre element. The spec gives an (informative) example:
The following shows a contemporary poem that uses the pre element to preserve its unusual formatting, which forms an intrinsic part of the poem itself.
maxling
it is with a heart
heavy
that i admit loss of a feline
so loved
a friend lost to the
unknown
(night)
~cdr 11dec07
However, I'd only use the pre element if the poem contains "more" than just meaningful line breaks (e.g. in this example the horizontal whitespace is meaningful).
If you have a simple poem, I'd go with the br element:
br elements must be used only for line breaks that are actually part of the content, as in poems or addresses.
container: p
For most poems, the p element is the right candidate (or severalp elements, of course). The spec has an (informative) example:
There was once an example from Femley,
Whose markup was of dubious quality.
The validator complained,
So the author was pained,
To move the error from the markup to the rhyming.
Also:
For instance, an address is also a paragraph, as is a part of a form, a byline, or a stanza in a poem.
structure: (article, figure)
Depending on the context (content, page structure, …), a sectioning element might be appropriate (article in most cases).
Also depending on the context, the figure element might be appropriate:
Here, a part of a poem is marked up using figure.
'Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.
Jabberwocky (first verse). Lewis Carroll, 1832-98
But don't use these in general for all poems, it really depends on the page if their use is correct.
misc. & trivia
someone proposed a poetry element (→ Rejected)
someone proposed a microformat for poems
discussion in the w3.org wiki: Explicit Markup to Semantically Express Poetic Forms (thanks for the link, steveax)
see also: on the mailing list
similar question on Webmasters SE: How to mark up a poem in HTML for SEO