Perfect Rhyme: Words that sound exactly the same from the stressed vowel onwards (e.g., cat/hat, night/light).
Near Rhyme (or Slant Rhyme): Words that sound almost the same, but not quite (e.g., moon/stone, love/move).
Eye Rhyme: Words that are spelled the same but pronounced differently (e.g., love/move).
Internal Rhyme: Rhymes that occur within a single line of poetry (e.g., "The cat sat on the mat").
End Rhyme: Rhymes that occur at the end of lines of poetry.
Masculine Rhyme: Rhymes that occur on a single stressed syllable at the end of a line. (e.g., cat/hat, night/light)
Feminine Rhyme: Rhymes that occur on two or more syllables at the end of a line. (e.g., flowing/going, tenderly/wonderly)
There are many other variations of rhyme used in poetry, as well as poems that do not use rhyme at all.