I once read a romance novel where every single chapter started with a quote from one of William Shakespeare's many works. To really drive the point home, one of the characters in the story was obsessed with the Bard; she, too, quoted him incessantly. Lots of books feature quotes at the start of chapters. I've also seen quotes from poems, songs and other books inside the text itself. Quoting is a great way to pay homage to someone else's work. It's also a great way to get yourself in serious trouble if you're a self-published author. Before you add quotes from songs, poems or other books to anything you're writing, make sure you're doing it without breaking copyright laws.
I've blogged about using brand names and celebrity names in self-published books in the past, and using song lyrics and other quotes is pretty similar. What I'm saying here is, you can get sued. Since you're not the creator of those lyrics, that poem or that other book, legally it's not yours to use -- up to a point.
If you've just got to use a quote or a lyric to really make your book's plot sing, you do have some wiggle room. There is something called the Fair Use law, and this states that authors (and other copyright holders) can use very brief portions of other copyrighted materials in their works. In other words, yes you can use song lyrics and quotes written by other people -- but only in very small amounts. The Fair Use law is purposefully ambiguous, in fact, and I can't tell you a certain stopping point you've got to hit. The law doesn't say you can only use 8 words of a song, for example. The law says you can use insignificant amounts, and if a copyright holder decides to take issue with something of theirs you have quoted the two of you may have to hash it out in court.
A certain criteria is used to determined whether or not use of copyrighted work falls under the heading of Fair Use: the purpose of usage, how much money will be made from the usage of the work, the type of work it is, how much of the copyrighted materials were used and the overall effect on the marketability of the copyrighted work.
You can always attempt to obtain permission to quote another author, poet or songwriter, however. Send an email and/or fax to them or to their representative explaining precisely what you want to use and how, but don't hold your breath waiting for a reply. You may not get one at all, and you should take that as a no if this is the case. You may simply receive a no, and in this case it's advisable to use none of that artist's material. If they say yes, obviously you're good to go.
And because I love finding the path of least resistance, I can offer you a workaround that makes quoting much, much easier: public domain.
No Law, No Problem
At some point, all great artists (and even not-so-great artists) die. That's a fact of life, and I'm sorry to bring it up -- but it is relevant. After the author of a work dies and a certain amount of time passes, the work they produced will eventually be deemed public domain. This means that copyright laws are no longer applicable. That means that you're free to quote away, and there's nothing that can stop you from it.
According to my resources, which may be sketchy and should absolutely be double-checked because I am not a lawyer, works created and published in the United States before 1923 are in the public domain. Anything produced after 1989 in the United States will remain protected for 70 years until after the author has died (not when the work was first published).
In other words, there's a whole bunch of stuff out there that you're welcome to use for free. Here's a list of public domain music you can quote all book long if you like. The list includes classic standards like "Danny Boy" and "When Irish Eyes Are Smiling." There's a great many Christmas carols that are public domain, including favorites like "Deck the Halls" and "It Came Upon the Midnight Clear." Quote them as much as you like.
And if you decide you want to quote Shakespeare a whole bunch? It's perfectly okay -- all of his works are in the public domain. However, as a general courtesy you should include the specific copyright information for whichever version of any song or book you use from which to pull your quotes and lyrics.