I am gonna post here some the very useful php libraries and classes which will come so handy during coding. You might run into various requirements which is why i compiled these php components.  All the php libraries listed below is free software and can be downloaded in the original authors website.

FPDF

http://www.fpdf.org/

FDPF is a free PHP library create PDF files with pure PHP.

PHP Mailer

http://phpmailer.codeworxtech.com/

PHP Mailer is a free class to send emails using PHP. It supports html and plain text email formats, including mail() and SMTP functions.

Autosuggest  Search

http://woork.blogspot.com/2008/03/php-components-autosuggest.html

PHP component to implement auto suggest feature in your textbox using MySQL.

ADODB Database Abstraction Library

http://adodb.sourceforge.net/

ADOdb is a database abstraction library for PHP designed for speed and portability. It supports number of databases including mssql, mysql, oracle, postgresql, and much more ..

reCaptcha

http://recaptcha.net/php/

Free PHP library to implement antibot captcha in your website for registrations. It is free service and works well with php.

phpThumb

http://phpthumb.sourceforge.net/

Very useful and light weight image manipulation library in PHP for generating thumbs in your website.

pChart

http://pchart.sourceforge.net/

A free php chart library to create numerous varieties of charts. Charts can be constructed from sql, csv, and from database datasets

Magpie RSS Parser

http://magpierss.sourceforge.net/

A PHP parser to extract fields from your RSS feed. It is easy to use without any difficulties.

PHP Text to Image

http://www.phpinsider.com/php/code/str2img/

A useful class which writes a text or string to an image.  Useful for hiding emails and for simple captchas. It can also output text inside an image at different angles.

Smarty

http://www.smarty.net/

A very popular templating engine for PHP. It is fast, lightweight and optimized for speed.

OpenID Login Authentication

http://www.openid.net

OpenID is a fastest and easiest code to implement login in your website.  This zend tutorial might help for implementing openID

HTML Purifier

http://htmlpurifier.org/

HTML purifier is an open source class for filtering mailicious and harmful XSS scripts. It is free library

jQuery

http://jquery.com

jQuery is a widely popular javascript library for event handling, animated transitions and interactions. It can be easily used with php for complex interactive web applications. Please see jquery PHP library to connect php to jquery

SAJAX

http://www.modernmethod.com/sajax/

Ajax framework for creating rich web applications. It easy to call PHP, Perl or Python functions from your webpages via JavaScriptYou.  Alternatively,  xajax which is as good as sajax.

UPU File Uploader

http://sourceforge.net/projects/upu/

UPU is a multiple file uploader class with progress bar. It is free software.

Univeral Feed Creator

http://www.ajaxray.com/blog/

Free PHP class which generates RSS and Atom feeds. Another useful class is  Feed Creator where you can quickly create RSS feed from MySQL database.

phpLib

http://phplib.sourceforge.net/

object-oriented application development toolkit for PHP. It is a free software for php programmers and developers.

CakePHP

http://cakephp.org/

Rapid PHP development framework for web applications.

PHP Excel

http://phpexcel.codeplex.com/

Free spreadsheet engine library to read and write excel, pdf, csv and html formats.

GeSHi Syntax Highlighter

http://qbnz.com/highlighter/

Geshi is a generic syntax code highlighter library supporting over 100 languages including PHP. Another alternative tool to highlight PHP code is phpCodeBeautifier

phpUserClass

http://phpuserclass.com/

Useful php library for user authentication and login management. It is a free open source project.

PHP Math Publisher

http://www.xm1math.net/phpmathpublisher/

PHP publishing system for publishing mathematical formulas. Each formulas are transformed into a image and it can be dynamically created. It works well in blogs, forums and with other content management applications.

PHP Image Upload & Crop

http://www.webmotionuk.co.uk/php-jquery-image-upload-and-crop/

PHP/JQuery image upload and cropping library. It needs GD library to be installed.

Smart Image Resizer

http://shiftingpixel.com/2008/03/03/smart-image-resizer/

Easy to use php class to crop and resize images on the fly.

GoogleMap API

http://www.phpinsider.com/php/code/GoogleMapAPI/

A library used for creating google maps using the Google Map public API. Features include multiple map markers, customizable icons, map directions built into info window, and sidebar generation.

IP to Country Lookup

http://www.eyesis.ca/projects/iplookup.html

Free php class to lookup ip address to country.

PHP Code Sniffer

http://matrix.squiz.net/developer/tools/php_cs

Useful library checks PHP code for programming violations and often used for testing PHP code practises.