There are probably as many different styles of boomerangs as anyone can imagine. They come in all different shapes and sizes (I’ve even seen one shaped like a kangaroo: a kangarang). Following are some from my collection.
3 of my boomerangs

Traditional boomerangs There is the traditional style that everyone thinks of when you mention boomerangs. These are the “L” or elbow-shaped boomerangs and are, obviously, named for their shape.

What many people don’t know is that there are also right- and left-handed boomerangs. What’s the difference? — the side on which the lift slope/angle is cut. Right-handed ’rangs have the slopes on the outer-left and inner-right arms. Lefties are just the opposite. Left-handed boomerang

X boomerangs Another style, or shape, is the X for four-blade boomerang. These are pretty much like throwing helicopter rotors through the air. Given that boomerangs work on basically the same principles as chopper rotors, it makes sense this style exists. These tend to be easier to throw and can often be thrown right- or left-handed.

Finally, there’s the Huh? category. Like the kangarang I mentioned earlier, these loopy fliers come in shapes you wouldn't think could fly like a boomerang. They range from triangular blades, like the Aerobie® Orbiter pictured to the right, to omega shapes, letters of the alphabet and just about anything any aero-engineer or physics major can think up. Aerobie® Orbitor

Regardless of the shape, size or style, they can be a lot of fun to throw. They’re also great exercise, especially if you’re a terrible thrower. You could even visit the following web sites if you want some ideas for making your own:

boomerangpassion.com

rediboom.com