Who needs clip art? A circle, a triangle, a square (the highlight), and a curvy line make a nice balloon. Repeat it a few times, changing the color and add a triangle bow. You could vary it even more by using an elongated ellipse for one or more of the balloons.
A checkerboard of squares is a versatile pattern. It could be a tile floor, a racing flag, or, as seen in the illustration, a tablecloth. Can you pick out the shapes used for the different eating utensils?
A simple shape (triangle) does more than just sit there. Can you tell what they represent in the above black and white logo design?
The SpiroBendo logo design in the illustration is nothing more than a rectangle, some circles, and some very thick lines with round ends (filled rectangles with rounded corners could work too) that combine to look like a spiral notebook.
Letters with a tail are fun. The tail on this Q (the circle) is a curvy line that does triple duty. It underscores the name, is the tail on the Q, and its curves suggest water — an obvious tie-in with the surf supply company.
Take the stack of circles from the Using Shapes illustration and turn 'em purple, add a "leaf" (distorted polygon shape), squiggly line, and some text for a nice logo. No art lessons needed.