If you took a peek at our "Form and Meter" section, or heck, even if you've just read the poem, you're already well aware of the rhymes in this poem. The end of every single line has a partner in rhyme. It's a regular rhyming riot.
But did you notice that there are also a ton of internal rhymes, too? These lines are often less obvious to us readers because internal rhymes occur within individual lines themselves. It's not about the big "ta-da!" that the end rhyme gives. It's a more subtle, musical effect.
Let's take the first line, for example:
They flee from me that sometime did me seek.
We've gone ahead and bolded and italicized the rhymes for you, just so they really pop. And lo and behold, there are four – count 'em, four – internal rhymes, which are those repeated "e" sounds you hear. This particular kind of internal rhyme comes from repeated vowel sounds, and we call it assonance.
Internal rhyme occurs yet again in lines 12 and 13:
And she me caught in her arms long and small;
Therewithall sweetly did me kiss
See how that "all" sound from the end of line 12 carries over to the beginning of line 13 in "Therewithall"? Neat, huh?
Of course these are just two examples, and you might find many more in the poem. You'll also find a lot of alliteration, or repeated vowel sounds at the beginning of words, like "softly said" (14) and "fashion of forsaking" (17). Plus, there are the relentless rhymes at the end of the lines.
In a sense, when you read it aloud, this poem sounds like a big old echo chamber. Practically every sound you hear bounces back to you in one way or another. This has the impressive effect of making our speaker seem supremely worried. All these repeated sounds make him sound almost obsessive, as if he can't get this scene with this mysterious woman, and his newfound lack of promiscuity out of his noggin. The sounds are beautiful, sure, but they're also strangely desperate.