What Resources Are Recommended for an Introduction to Signal Processing (DSP)?
My recommendation in terms of text books is Rick Lyons's Understanding DSP.  My review of the latest edition is here.

I, and many others from the ${\tt comp.dsp}$ community and elsewhere, have helped Rick revise parts of the text since the first edition.  

For self-study, I know of no better book.

As an on-line, free resource, I recommend Steve Smith's book.  Personally, I prefer Rick's style, but Steve's book as the advantage of online accessibility (and the online version is free!).



Edit:

Rick sent me some feedback that I thought I'd share here:

For your colleagues that have a copy of my DSP book,
I'll be happy to send them the errata for my book.  All they have 
to do is send me an E-mail telling me (1) The Edition Number, 
and (2) the Printing Number of their copy of the book.  The Printing 
Number can be found on the page just before the 'Dedication' page.
My E-mail address is:
R.Lyons [at] ieee.org

I recommend that your colleagues have a look at:
http://www.redcedar.com/learndsp.htm

Rick also gave me a long list of online DSP references.  There are way too many to put here. I will see about setting up a GoogleDocs version and re-post here later.