First, a good logo is simple in design but complex in theory. This means that the logo itself is fairly basic on the surface however the image carries a deeper significance overall. Twitter is a good example in this instance where they use a simple blue bird for their logo. However looking closely at the blue bird you can see the birds beak is slightly open indicating the bird is in the process of tweeting. Contrast that with what Twitter does - short messages that reach a wide audience you have a perfect synergy in messaging.
A great logo is quickly identifiable, such as the McDonalds logo. The golden arches of McDonalds is known worldwide as one of the most popular fast food restaurants. Interestingly, the golden arches don't necessarily identify with food but rather a large "M". This also demonstrates that the logo doesn't necessarily need to identify directly with a particular market versus a particular brand.
Lastly, a logo is memorable such as the Nike dash. Not only is the Nike logo simple and quickly identifiable but is memorable. The dash identifies so strongly with speed and athleticism that is nearly impossible to forget.