1. Sams teach yourself php in 24 hours (excellent book with some fundamental things we need to know, taught me a lot and i still occasionally look at it now).
2. peachpit press, 'php and mysql' quickstart guide (not as good as the others, they use old syntax etc)
3. sams php and mysql web development (this IS what i classed as my bible, its on its third edition now, id strongly recommend this book, absolutely great, taught me an awful lot of what i know today)
4. developers library advanced php programming (this book is quite hardcore, not too many php examples etc but has a wealth of information avout design patterns etc, 'a practical guide to developing large scale php applications' - damn good read!)
5. sybex (php freaks' eric rosebrocks book) 'creating interactive websites with php and web services' (i brought this solely because it was erics first book, to be honest its not the best book i have, but has some great chapters, plus a lot of it is familiar beacuse i have been a phpfreak for a few years now..)no disrespect to Eric what-so-ever!
6. oreilly php pocket reference - nice little 'pocket sized' (!) book outlining all f the php functions etc - nothiing that cant be found on the net but for £7 its a must have, i keep it in my laptop bag (along with apache pocket ref and mysql pocket ref - good books)
I would recommend sams or oreilly, you can guarantee a quality book from them. 99% of the books i have are by these guys and 95% of them are excellent books. stay away from the 'visual quickstart guides' (peachpit press) - it seems they write books a few years behind everyone else!
Stuart / theverychap.
i like to add 'PHP and MySQL Web Development' by Luke Welling and Laura Thomson to the list of recommendations.
It's not lame, neither is it hardcore, but it teaches you things from simple 'Hello World' scripts right through to developing content management systems, email programs, etc.
It's pretty much written in 'English' speak too, not programmers speak, so people of all levels will easily find it useful.
The book I first bought was called PHP Fast and Easy Web Development
Actually the only book I ever bought, the rest I learned from applying it, trial and error, and asking a lot of questions here
Here's an amazon link to it
If you have any other books to add or you'd like or get more information on one
check out this post