Designs I tend to like possess some or all of these traits that I like to call the three Cs.
They are Clever and make you go, "Ohhhhh...! That's pretty cool!"
They have Clarity and aren't bogged down by a myriad of random or distracting elements.
They are Communicative and create either an intriguing narrative or gets the point across succinctly.
Here are some examples of designs that I found were appealing to me.
This is a logo for The Swan & Mallard Restaurant and it utilizes negative space in a creative way. The swan, mallard, and ampersand are all one element.
This logo is, in my book, a CCC. Triple C!
This is a very creative logo for a pet store called Feathers & Fur. The figure is both, at once, a dog and a bird. Clear, succinct, and creative.
CCC.
This logo is similar to the first two in concept. A golfer and profile of a Spartan warrior is combined to form the logo.
Some examples of design I don't particularly like or care for:
This one suffers from poor spellchecking/proofreading, making it hilariously bad.
This is at the T Deck parking garage at GSU. The sign almost reads "Exit addtional parking". I think it can be improved by being split into two signs: one that says exit, and another that says additional parking.