Niklaus Wirth's _Compiler Construction_ (free online, http://www-old.oberon.ethz.ch/WirthPubl/CBEAll.pdf) has a good intro to parsing, though for better or worse it's skewed towards recursive-descent parsing and has a "hit the ground running / focus on theory later" style.
After that, you could dig deeper with Andrew Appel's _Modern Compiler Techniques in {ML,C}_ books. The ML one is better, IMHO. Those cover other methods (LL, LALR, SLR, etc.) in greater detail, and I'd also recommend either for learning compilers in a heartbeat. (Appel's _Compiling with Continuations_ is also excellent, but doesn't cover parsing.)
Following that, Dick Grune's _Parsing Techniques: A Practical Guide_ (http://www.few.vu.nl/~dick/PTAPG.html) is a good reference...and thorough. If you're reading it to learn the basics, it might seem a bit dry, but I think it's at a sweet spot between depth of coverage and deference to the extensive bibliography. I have the second edition; the first is free online. Not sure about the differences, but the coverage of fundamentals probably haven't changed much. Also, while the other two are compiler books with chapters on parsing, this one is 100% parsing, and gets to a lot of interesting parsing algorithms (e.g. Earley parsing) that don't usually get much love in compiler texts.
Some people will also recommend the Dragon book, but I think those three will be more helpful. I haven't read the new edition, but the old seems drier & less thorough than the Grune book, less direct than the Wirth book, and less modern than the Appel book.
Also: For learning lex and yacc, the intros in the _4.4BSD Programmer's Supplementary Documents_ ("PSD", included with OpenBSD and probably the other BSDs, and not hard to find online) are hard to beat. The O'Reilly _Lex and Yacc_ book somehow manages to be roughly ten times as long yet less informative.
And if you have full control over the syntax used, S-expressions (Lisp), RPN (Forth), or Lua/JSON will let you dodge the issue of parsing entirely.
That is likely the most thorough, informative response I have ever received. I almost qualified that with "on the internet", but then I realized, hell, it's probably more informative than any response I've ever received anywhere.
I recently saw a news piece about a philanthropist helping people in poor African villages by simply building wells. The tribesmen were so grateful, one said "I wish he lives one hundred and fifty years so that he can continue helping people like us."
Well, Scott, thank you. I hope you live one hundred and fifty years.
There's some real gems in the archives here. For starters, see http://news.ycombinator.com/item?id=835020 . More generally, try googling site:news.ycombinator.com keywords.
And, thanks. :)