I’ve actually seen a few folks go to create a logo for themselves and start drawing pictures.
When you see a picture next to the logo, that is called the trademark. Many companies include a trademark to go with their logo but some of the best and most effective logos rely on the type by itself. For example, Coca Cola.
Once the logo becomes well known, the trademark might be able to stand alone. An example of this would be the check in the Nike logo or the Apple for Apple products.
When you are just beginning to design a logo for your business, pay attention to the typography first. Keep it simple. Think about how it will fit on all types of media.
Here’s a fun look at a logo coming to life.