To bear in mind the colours of the rainbow (purple, orange, yellow, inexperienced, blue, indigo, violet), do this man’s title:

ROY G. BIV

For naming the planets so as from the solar (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto):
My Very Easy Memory Jingle Seems Useful Naming Planets

The organic taxonomy (Kingdom, Phylum, Class, Order, Family, Genus, Species):
Okayings Play Cards On Fat Green Sinstruments

The arithmetic order of operations (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction):

PEMDAS

To bear in mind the colour codes on resistors, capacitors, and different digital parts:
Bproper Boys Rave Over Young Girls But Veto Getting Wed

Medical college students can bear in mind the 12 cranial nerves with:
On Old Olympus’ Towering Top, A Finely Vested German Viewed A Hawk

The fundamental trig features (sine=reverse/hypotenuse) (cosine=adjoining/hypotenuse) (tangent=reverse/adjoining):

SOH CAH TOA

The nice lakes of North America (Huron, Ontario, Michigan, Erie, Superior):

HOMES