At some point in your life, you probably were told that some words had no rhymes. This isn't really in dispute. For example, orange and purple. You were probably also told that only a few words end in 'gry'- angry and hungry. They don't rhyme, so they can't have rhymes, right?
Well, first off, there are more than a few words that end in gry. They're just not commonly used. Several of the words counted in the link cheat by being two words that end with a hyphenated -angry or -hungry, but a lot more count legitimately, including 'gry' itself, which means either a small measurement, or anything of little value. Other words, such as scavengry, meagry, and managry, take the same approach angry and hungry do: use 'gry' as a suffix to say that someone or something is acting like the base word: anger, hunger, scavenger, meager, manager. Angry and hungry are just the only words that avoided falling into the realm of the archaic.
One of those words, 'rungry', rhymes with hungry, although that list appears to be the only place 'rungry' even counts as a word and not a part of someone's Scooby Doo imitation. Angry still has no rhyme, though.
As for orange and purple, they both have rhymes too. Orange has 'sporange', a form of sporangium, which is where spores get formed. Purple has two. There's curple (which is, to put it bluntly, a horse's ass), as well as hirple (walking with a limp).
A lot of other common words with obscure rhymes can be found at this Wikipedia page. Silver, for instance, rhymes with chilver, a female lamb. Circle rhymes with hurkle, a word meaning to pull in all your limbs, as if to cower. Pint rhymes with rynt, a word milkmaids use to order a cow to move after they're done milking them. Month goes into the realm of the mathematical to find its rhyme with 'oneth', as in something like 'hundred-and-oneth', which is obscure because you'd just say 'hundred-and-first' instead. Music has, among a couple others, ageusic, which means someone who doesn't have a sense of taste. Plankton rhymes with Yankton, a branch of the Sioux tribe.
I'd go on, but even to me this is starting to become very gry.