You DO sign a cover letter.
The formal format for a cover letter includes a both a typed signature and an ink signature. Adding a handwritten signature (not a script font from a word processing program) personalizes your cover letter. By omitting the signature, you run the risk that it may seem like an oversight or carelessness to the recipient.
The correct format for a signature on a cover letter is as follows:
At the conclusion of your succinct 3-5 paragraph cover letter you should place a complimentary closing (ie. sincerely, regards, etc.). Skip three spaces then type your full name. Sign your name in ink between the complimentary closing and your typed signature.
“Purdue OWL: Cover Letters 1: Quick Tips .” Welcome to the Purdue University Online Writing Lab (OWL). N.p., n.d. Web. 17 Nov. 2011. http://owl.english.purdue.edu/owl/resource/549/03/
“Common Cover Letter Mistakes.” Washington State Governement. N.p., n.d. Web. 17 Nov. 2011. www.wa.gov/esd/guides/resume/letter/letter_commonmistakes.htm