Although most people seem to restrict themselves to one kind, there are actually many different types of poems. The main poetry types are free verse and rhymed verse, but within these two subdivisions there is an incredible amount of variety. Free verse is a great place to start if you're unfamiliar with poetry. It is the freest type of poetry because there are no rigid structures for form or content. You can make it as long or short as you want to, use internal rhymes when you want, or even write it in paragraphs. This incredible freedom allows you to explore your creative powers to your full potential.
Of course many of the most cherished types of poetry are varieties of rhymed verse. Sestinas, sonnets, and other meters all have their advantages. One of the great things about practicing rhymed verse poetry is that it can teach you a lot of discipline in your language. With free verse, you have so much freedom that laziness can be a temptation. You don't really need to find the perfect word to make a poem fit. After all, there are no requirements for the structure. With rhymed poems, however, you have to work a little bit harder. You have to make sure that the meter matches as close as possible, and find the perfect word for every situation.
Then there are types of poetry that don't fit neatly into either of these categories. Haiku is one example of a strange type of poetry. Haikus do not have to be rhymed, but they do have to have a certain structure. Each line needs a certain number of syllables for it to be a proper haiku. This can be a great type of poetry for experimentation. Haiku is short that you can come up with several different poems in a short period of time. This allows you to try to figure out what works and doesn't work in poetry.
Thinking about it, I would have to say that I don't have favorite types of poetry. For me, what matters is the quality of the individual poem. Some of the poems I like are quite classical, written in very structured verse. Other ones are pretty avant-garde and flowing, using a free-form structure that is more like jazz than like sonnets. I have seen people do great things with many different types of poetry, so I don't really exclude any of them. If it sounds good, I will enjoy it.
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