A couple of moodboards I made for a game were going to make.
I don't own the rights to ANY of the pictures.

Gothic
Lots of curls and overly decorated
Dark colors, reds, purples, greens, browns, blacks, blacks, blacks etc.
Vampires and politics

Colorful games
Round
Bright colors
Weird shapes
Surreal
Deformed characters instead of correctly porportioned characters

Kawaii Japanese style
Big eyes
Lots of white and pink
Give something eyes and it's cute
Make everything cute (so just give everything eyes)
Huge heads, hands and feet without toes or fingers
Symbols

Paper 'n fabric (I had this one because of a school assignment so I just threw it in.)
Three dimentional but still 2d
Use lots of paper and fabric textures
Looks playful
Difficult to make sprites from

Steampunk
Red woods
Copper
Gears and cogs
Weird meters
Airships and land ships instead of/or in addition to waterships
Parchment with complicated drawings
Round windows
GOGGLES

American comic
Flat colors
Dotted images
Text balloons
Awesome sound effects

Pixel art
Awesome
Lots of work/difficult to do right and generate a lot of content
Classic game feel

Cell shaded
Black lines around everything
Cool when gritty (second top picture from the left)
Also possible in cartoon variant (second lowest picture from the left)
Very versatile
Awesome in 3D sprites
I think you can just use a cartoon shader for this and it looks awesome easily (when done right...)

Classic ghost/zombie pirates
Just plain awesome but maybe done too often
Dark ships
Rotting and rusted boats
Skeleton pirates