Serif fonts have the little squiggly items at the end of the letters. There is a reason for this...it increases readability of the text. It creates a natural flowing together of the text that makes it easier on the eye. When we read, we don't read letter per letter like "H-A-R-R-I-N-G-T-O-N," but rather, our eyes recognize groups of letter combinations in certain words, so it's really more a case of syllable by syllable rather than by each letter. Fonts that do not have serifs can be hard to read when you are reading large blocks of text.
Being that the logo is usually just one word or a small group of words, it doesn't make a significant difference which type of font is used...it's really an issue of style and preference. Some classic styles in this typeface are: Times, Trajan and Palatino. See the graphic above.
These two typeface fonts can be mixed and matched in the design process, where the initials of the company name might be in a serif font and the spelled-out name below might be in a sans-serif font.