One rhyme to remember the planets is "Amazing Mercury is closest to the Sun, Hot, hot Venus is the second one, Earth comes third; it’s not too hot, Freezing Mars awaits an astronaut, Jupiter is bigger than all the rest, Sixth comes Saturn, its rings look best, Uranus and Neptune are big gas balls, Tiny Pluto is the last planet of all." As well as using rhymes to remember the order of the planets, there are also a good selection of mnemonics available.
"My Very Educated Mother Just Showed Us Nine Planets" uses the first letter of each planet, replacing the names with words to help remember the order of the planets. It does of course include Pluto, a dwarf planet that has been removed from the roster of official planets. A mnemonic to remember the planets without Pluto is "My Very Eager Mother Just Served Us Nachos."