Hopefully posts like these aren't off-limits for non-moderators. I just felt that these manual pages were the most important ones to read and that they should bring just about any newcomer up to speed very quickly on the fundamentals and some not-so-fundamental but still important topics.
The Language reference page: http://www.php.net/manual/en/langref.php
The pages linked on this page are absolutely necessary. They'll teach you about all the time-saving goodness PHP has to offer. Things you may never have heard of, or things you've seen but never understood in someone else's source code. Arrays, switches, all the loop types, and a bunch of other things that'll help you write smarter, faster, and clearer PHP applications.
String functions: http://www.php.net/strings
PHP is a Web-programming language and as such, it's all about handling input and output and stored data. Strings are everywhere, and PHP has some very awesome functions for doing all sorts of handy and cool things to them. If you're looking to do some really fancy things with strings, check out the Regular Expression section at http://ca.php.net/pcre. The "Pattern Syntax" page will teach you how to write regular expressions (though there are other, more casually-worded tutorials on the Web that you might want to Google for).
Array functions: http://www.php.net/array
You've learned about the array in the reference and now this page will show you the vast number of time-saving and just plain necessary functions for sorting, splitting, merging, etc.
Some of these you may never use. Others you may use all the time. round (), abs (), ceil (), and floor() are just some of the ones everyone needs to know about.
This isn't as necessary as the others, but when you've got a firm grip on the rest of the stuff listed here, you'll probably want to dive into the awesome world of databases. The MySQL page lists the functions and examples you'll need to get going. To get started on SQL, I've always liked www.sqlcourse.com and www.sqlcourse2.com for graduates of the former.
That about does it for the pages I think are most necessary. Please contribute your favourite manual pages, too. Hopefully this thread will help a lot of confused or frustrated or just plain ambitious PHP newcomers.