If you think of a poem as being like a piece of music, the meter is like the bass and the percussion, that give the music its sense of rhythmic stability. But a musical composition needs more than a percussion section, and a poem needs more than meter. It needs some coloration of sound. Alliteration and rhyme can help out with that.
 

Alliteration

Alliteration is a repetition of initial sounds in words. Depending on the sound repeated, this can result in some very different tonal results. For example, if you're repeating an "s" sound, you may end up with a poem that sounds eerie, mysterious and sibilant. If, on the other hand, you're repeating a more abrupt sound like a hard "g" or a "k" sound, the result could possibly sound more comic. Below you can find an example of each:

• Snow streaks swiftly across the still, silent sky.
• Gregory gives goofy gifts while guzzling from goblets

Alliteration is a powerful tool to add some interest to your poem, but beware - overusing it can ruin your poem (unless you're trying to be comical; there doesn't seem to be an upper limit in that case!). So don't just write your alliteration -- read it out loud and really listen to it, to make sure you're not over doing it. My rule of thumb is, if I'm consciously aware of it, it's probably too much.

Here's a poem I wrote which relies on alliteration. The poem is also published at Fifteen Minutes of Fiction. Can you find the alliterative words?
 

Rhyme

Rhyme is a very popular way of adding coloration to your words. In fact, it's so popular that many people think poetry must rhyme. Rhyme is the repetition of ending sounds, instead of sounds at the beginning or the middle.
 

• blue, flu, anew, clue
• yellow, fellow, bellow
• fable, table, sable

Most often rhyming words are used at the ends of lines:
 

Remember that I said overusing alliteration can ruin the feel of your poem? Well, the same is doubly true of rhyme. I'd rather listen to a poem with no rhymes than a poem that has rhymes that slap you in the face. So read your poem aloud, and really listen to how your rhymes sound!

Slant Rhyme

Slant rhymes are more subtle than normal rhymes; a slant rhyme is a pair of words that almost rhyme but don't quite. I remember, as a kid, singing a hymn in church that had some slant rhymes:
 

If you study the other verses of the hymn, you'll realize that the words at the end of the first and third lines rhyme. But "name" and "diadem" do not rhyme. Instead, they are "almost" rhymes. And they work very nicely. If done well, a slant rhyme is subtle -- if not done well, it can stand out like a sore thumb!
 

Assonance

Assonance is repeated vowel sounds within words. Beware: this is not the same as repeated vowels; remember that a vowel which has one sound in one word may have a different sound in a different word.

Assonance is usually more subtle than either alliteration or rhyme; because it comes in the middle of the word instead of the beginning or the end, its a little more hidden.
 

• Certain purple fabrics make great curtains.
• A little bit of fidgeting makes silly kids snicker.

In the first sentence, the "ur" sound of "certain," "purple," and "curtain" is repeated. In the second, the short "i" sound is repeated.