The person who introduced me to Perl showed me that ... well, in my case it's kinda of a spurious question, considering that no-one really properly introduced me to the language. At the time, I just happened to look around for a good scripting language to learn and saw that Perl was one of the languages used by some members of my team. I bought the Camel book, dived in and... the rest is pretty much history.
I first starting using Perl to do small shell stuff. If I recall correctly, the first script I touched was a load balancer that was monitoring a unix corral and launching queued jobs on the less busy machines. Then I began to use it to diddle text files (change 'class Foo' to 'class Bar' in my source code, figure out how many functions are in each file, etc.). And then came the Solitaire 500. My entry to the contest shamefully crashed and burn at the starting line, but I still managed to squeeze a t-shirt and a love of the language out of the experience. To this day, I still have both (although one is pretty much due for replacement).
I kept using Perl because it is so much damn fun. Most other languages are like station wagon cars. They get you from A to B, but they are not much to write home about. But Perl... Perl is like James Bond's car. Beside the driving wheel, you have a red button here to activate the flamethrowers. Below the glove compartment -- yes, you see right -- there's a lever that engages the retro-propellers. And it doesn't end there: if one was to ever get bored with all those nifty toys, Q still comes up regularly with new features.
I can't stop thinking about Perl for the same reason a rock star can't stop thinking about his Fender Stratocaster XII.
I'm still using Perl because I have yet to find another language that is so delightfully idiosyncratic and yet so practical. Or that has such a striving community. Or that has anything remotely comparable to that magnificent temple dedicated to Aergia that we call CPAN.
I get other people to use Perl by asking them what task they want to achieve, and doing it before their eyes in a handful of lines. Once I have thus acquired their awestruck attention, I reel them in for my weekly Perl Lunch'n'Learns where the true corruption can begin.
I also program in TCL and Javascript, but I like Perl better since it doesn't make me want to drive red-hot tetanus-laden nails through my prosencephalon. Javascript is not that bad, mind you -- I actually like it. But nothing, nothing, can shear such deep gouges in one's psyche like badly written TCL can. And this is coming from someone who known Intercal, brainf*ck and VisualBasic...