(based on link below, see it for fuller definitions and examples):

Perfect rhyme (all sounds match from at least vowel of stressed syllable on)

* Masculine rhyme (last syllable stressed)

* Feminine rhyme (earlier syllable stressed)

* Identical rhyme (same words, different meanings)

* Rich rhyme/”rime riche” (word and its homonym , sea/see)

* Macaronic rhyme (words from different languages)

Near rhyme (half, slant, approximate, off, oblique)

* Assonance (matches only vowels – update/subway)

* Consonance (matches only consonants – miss/mass)

* Light line (stressed syllable with secondary stress)

* Wrenched rhyme (stressed syllable with unstressed)

Eye rhyme (spelling matches, not sound)

http://www.poemofquotes.com/articles/rhyme-glossary.php

For other classifications see:

http://en.wikipedia.org/wiki/Rhyme#Types_of_rhyme

http://en.wikipedia.org/wiki/Peter_Dale’s_classification_of_rhymes

“Partial rhyme” is “close enough for poetic license” (fault/ought)

“Eye rhyme” is a rhyme that does not exist in sound at all, “but only in sight (tough/cough)

“Half rhyme” is a match between final consonants, but a miss on the vowels (bits/bats)

“Masculine rhyme” is one-syllable rhyme (near/clear)

“Feminine rhyme” is a rhyme of more than one syllable, both stressed and unstressed (creature/feature)