Oh I had to answer this question for my management ever so recently and can give you a quick breakdown.
Database Interfacing. PHP is made to interface with just about any database out there. ASP is picky and tends to only want to work with Microsoft stuff.
COM calls. Every time ASP needs to do something, it uses a COM call and the more you do and more complex your program, the more COM calls. This can slow things down immensely. PHP doesn't even deal with COM but works equally well with IIS as it does with Apache.
Cross platform compatibility. If you build a whole bunch of apps in ASP and then your system get hit by the latest worm and management decides to convert everything over to Linux, you're hosed. PHP on the other hand is cross-platform compatible. In other words, your scripts built on an ISS web server on Windows will still work equally well on an Apache web server running on a Linux box.
Speed. PHP is by far leaps and bounds faster than ASP. And it can be compiled as an Apache module making it 10-20% faster. AND you can even add a flash memory cache making it even 40% faster than that. You can't compete with PHP in this manner.
Syntax. If you are familiar with Perl, C, C++, java, javascript then PHP is a snap to learn because it uses similar functions. ASP is much different, takes a longer learning curve and requires support languages to get anything done.
No additional languages required. Even though you may know ASP, it also requires you to use VB or Jscript as a support language (which also adds to the COM calls) . In PHP, you can do it all with one language.
MySQL. This should be reason enough. Mysql 4.0 is an open sourced RDBMS and in recent independent benchmarks, ranked equivalent to Oracle 9i in the speed category. And PHP is MADE to work with MySQL. MySQL is the perfect web delivery tool and PHP is it's pimp. Can you feel the love?

Community. Need to ask a question? Jump on any forum. Need a script? Just download one from sourceforge, freshmeat or a million other sites. Try getting this kind of support from ASP online. Hell, you can't even find good documentation on the MS site.
Web Servers. If you are unfamiliar with Netcraft.com, it keeps statistics on the web and web servers. As of currently, 64% of the web runs Apache and since apache can't run ASP, PHP is the scripting language of choice. In comparison, 24% of the web runs Microsofts IIS and, I can attest to this, PHP runs on IIS just as well.
These should be reason enough to use PHP 

