If I wanted to start a greeting card company and use famous quotes
from poets, authors, or musicians (lyrics from their songs) and quote
them on the front of a greeting card, would I be violating any law if
I credit the writer (musician)? Would I need specific permission from
anyone?

Example: "From the very first time I set my eyes on you girl, my heart
said follow through." -Bob Marley    or   "I have found that if you
love life, life will love you back." -Arthur Rubinstein

Dear Muse, 

Before I begin to answer, I'd like to direct you to the disclaimer on
the bottom of this page: "Answers and comments provided on Google
Answers are general information, and are not intended to substitute
for informed professional medical, psychiatric, psychological, tax,
legal, investment, accounting, or other professional advice". In other
words, I am not giving you advice as a lawyer, and if you feel that
you need a professional legal advice, please contact an advocate.

There are two points here - whether quotes are protected by copyright,
and whether your usage of these quotes would violate them.

First of all, quotes are protected by copyright, and I'll explain. The
quote is taken from somewhere: a song that the person has written, a
book, an interview - it has been published somewhere, and the
publisher - the song writer, the journalist who has written the
article or their journal - they have the copyright.

You can read more about copyright law here: 
<http://www.copyright.gov/circs/circ1.html> 

As mentioned before, if you contact the copyright owner, this is not a
problem. However, acknowledging the source of the copyrighted material
does not substitute for obtaining permission. Another possibility is
to use only quotes that are older than 70 years. Shakespeare or Marx
are not protected by copyright; neither are many other written texts
and poems. See, for example, books that are included here:

Project Gutenberg
<http://www.gutenberg.org/> 

In addition, if the quote is part of a commentary or a parody, you
might be able to claim for "fair use" within the protection of the
law. Nevertheless, this is tricky and might get you in a legal battle,
even if you'll win at the end.

Fair Use
<http://www.copyright.gov/fls/fl102.html> 

I hope this answers your question. Please contact me if you need any
clarification on this answer before you rate it.

Great answer. Very helpful. Thanks so much.

If the lyrics or poems are contemporary, then you will have a
copyright issue. That is not to say that you will not be able to
license an excerpt of the lyrics for your card, but just that you will
have to pay. For example, I wanted to use a few lines from Irving
Berlin's song "Blue Sky" in a book that I published. I contacted the
Music Publisher, Irving Berlin Music, and we negotiated a fee for that
use. Some times you will be asked for a flat fee for unlimited use
while others may limit the number of cards that you can print for x
amount of dollars. My advice to you is to choose what you feel to be
your 10 best uses of lyrics and then approach the publishers with an
offer that makes financial sense to you and your business. They can
only say "no" and if they do, chances are you will receive a counter
offer. There are some lyrics and poems that you will never get the
rights to use. Any Lennon-McCartney work would not be a possibility or
any of the top poets. I tried to license an E.B. White poem for
inclusion in one of my songs and it was a loud and decisive "NO". You
might look to some songs or poems that are in the public domain
although that may make it harder for you to sell to the younger
demographics.

"Fair use" will not cover your producing and selling cards.

"Section 107 of the Copyright code (commonly called Fair Use) limits
the rights of the author, allowing parts of a copyrighted work to be
used without requesting permission. Such circumstances are limited to
criticism, comment, news reporting, teaching (including multiple
copies for classroom use), scholarship, or research. Nevertheless,
Fair Use is NOT carte blanche to use any amount of a copyrighted work
for any amount of time just because it is "for educational purposes.
..."
www.washburn.edu/copyright/glossary/

Thank you for the rating and the tip!