There are three types of logo – text, symbol and a combination of the two.
A text logo is used when the client’s name is long (Marks and Spencers) or unique (Yahoo!, below right).
A symbol logo is the opposite. An example of this is Nike’s “Swoosh” (right) which, by-the-way, originally cost Nike only $35 – no words or letters just shapes. This is usually used for companies that already have a high profile. MacDonalds have their arches, Microsoft has it’s wavy window and Apple has its … apple. This is where logos reach the lofty heights of icons.
And finally, a combination logo is a union of text and symbol. It also can be a combination of logo and slogan.
Two things I’ve noticed for the future. Photoshop has brought a newer looking style of logo using its gaussian blur – for example Tate’s logos. And the use of transparency in Illustrator has introduced overlapping elements in logos. Expect to see more of these in the future.