Rhyming is language played with. To be able to write lines that rhyme takes skill and a willingness to bat words around, form and re-form them into pleasing shapes all while creating a picture in the mind of the reader.
The best rhymes create more than one picture. They can be funny, pithy, convey truth, pathos, be sung, be performed, but above all, they exult in the language and its usage.
My favorite poet is Ogden Nash. He is known for his use of humor in his poems, and for making up words (like “Bryaness,” above). But what I like most about him is his economical use of language and the way he can make something funny with a twist:
The Porcupine by Ogden Nash
If you are a wordsmith and enjoy poems, I found a site called Vhinkle that has a nice little glossary of poetry terms, here. You might just lose an hour or two poking around and writing your own examples, so be warned.