I have an old Pentium II 300MHz PC from the late 90s with 128MB of memory. I'm not sure when exactly it was first purchased, since I first got it second hand off of someone else in 2003. I added a new ethernet card in 2003 when I got it, and the CD drive has been replaced since, but other than that it's the original hardware (including 15" CRT monitor). The hard drive died long ago, but it doesn't need one to do its job.

And yes, it is used in production, for one very special task:

I'm the author of Gargoyle Router firmware (www.gargoyle-router.com), an alternate firmware for wireless routers. I've recently started selling some small routers with my software installed, but loading each one individually takes some time -- about 10 minutes each. This 10+ year old system runs a customized version of Knoppix, which can be used to install my software onto a large number of routers simultaneously. It means I can flash as many routers as I want within 10 minutes, instead of having to wait for 10 minutes each. This multiplex install system has some other components as well, but this PC sits at the center of it.

It's far more convenient to have a separate PC (especially one with a monitor) for this, since that way I don't have to keep disconnecting/reconnecting the necessary ethernet cords. Also, it only draws power during the brief time it's turned on (when I'm actually doing an install), so the fact it has an inefficient power supply isn't really a problem. It's cheap and it works, which is what matters.

edit: It was 2003, not 2002 I first bought the system.