Reddit reviews Poetry 180: A Turning Back to Poetry

Poetry 180 is a good beginner's anthology. It was made when Billy Collins was poet laureate for the U.S. and provides a host of contemporary poems that are not too difficult to get through.

http://www.amazon.com/Poetry-180-Turning-Back/dp/0812968875

Another anthology that I enjoy is the The Best of American Poetry especially the 25th edition which incorporates poems from the past 25 or so years. You'll find stuff in there that you'll hate (i.e. why is this even in here?) and some stuff that you'll fall head over heels with.

http://www.amazon.com/Best-American-Poetry-Anniversary-Edition/dp/1451658885

Other than that I'll second Norton's but it's a bit heavy for a beginner.

For simple to understand poetry that still has a point, there's a collection by Billy Collins that I absolutely love called "Poetry 180." I think that the intent of the book was for it to be an introduction to poetry accessible to high schoolers. It has a lot of short, pithy poems that I still think a lot about.

http://www.amazon.com/Poetry-180-Turning-Back/dp/0812968875

I'd suggest starting with poems that are relatively brief, highly readable, and modern -- really get a taste for how poetry can be relevant to your everyday life. There are a ton of good books out there dedicated to poetry of this type, such as Garrison Keillor's Good Poems, with poems like Mary Oliver's Wild Geese:

You do not have to be good.
You do not have to walk on your knees
For a hundred miles through the desert, repenting.
You only have to let the soft animal of your body
love what it loves.
Tell me about your despair, yours, and I will tell you mine.
Meanwhile the world goes on.
Meanwhile the sun and the clear pebbles of the rain
are moving across the landscapes,
over the prairies and the deep trees,
the mountains and the rivers.
Meanwhile the wild geese, high in the clean blue air,
are heading home again.
Whoever you are, no matter how lonely,
the world offers itself to your imagination,
calls to you like the wild geese, harsh and exciting --
over and over announcing your place
in the family of things.

Oliver has also written a Poetry Handbook which discusses the technical aspects of poetry like rhythm and form, and illustrates the principles with poems generally considered to be modern classics, if you're looking for something more technical.

Keillor also does the The Writer's Almanac on NPR, and you can go to the Writer's Almanac site for a (usually) good poem each day. Other good starting points include Billy Collin's Poetry 180 and Hirsch's How to Read a Poem and Fall in Love with Poetry.

I'm also a fan of Catherine Bowman, who's a bit obscure (she's the Poetry... um... person for NPR's All Things Considered) and so I'm going to post one of her poems (Broke Song) because I'll probably never have another chance to do so as smoothly as I am clearly working it into this post.

You move through the world broken. Navigating
by the stars encoded on your hearts axis. July
grasses. Rain. How the world breaks us.
Midnight scatters across what’s left
from an evening prayer. The broken
song of the warbler at dawn
on the last day of winter. You move
through the world gathered
together in a pulse. Running your fingers
up and down what is odd and so familiar.
How dazzling the fit. To be remade
by the glue of your oaths and kisses.

Edit: Also, Robert Bly.