Fan constantly running

Reset the SMC.
http://www.apple.com/support/macpro/

And make sure that it is in a ventilated location (not recirculating out air out the back and against the wall).

Boost the fan speed manually, and monitor the temperature readings.

I am waiting for Apple to release silent fan-less computers! It is entirely possible using Stirling Engine - WIKI excerpt:

The first Stirling-cycle cryocooler was developed at Philips in the 1950s and commercialized in such places as liquid air production plants. The Philips Cryogenics business evolved until it was split off in 1990 to form the Stirling Cryogenics & Refrigeration BV,[63] The Netherlands. This company is still active in the development and manufacturing of Stirling cryocoolers and cryogenic cooling systems.
A wide variety of smaller size Stirling cryocoolers are commercially available for tasks such as the cooling of electronic sensors and sometimes microprocessors. For this application, Stirling cryocoolers are the highest performance technology available, due to their ability to lift heat efficiently at very low temperatures. They are silent, vibration-free, and can be scaled down to small sizes, and have very high reliability and low maintenance. As of 2008, cryocoolers are considered to be the only commercially successful Stirling devices.

I am having a problem with my fan running **** near constantly. Here's a screenshot of my computer's environment:

http://timmy.vox.com/library/post/hot-or-not-a-cpu-temp-question.html

I should note that this is when all apps are off.

How hot is too hot? How much fan is too much fan? It seems to be getting worse and I am very worried for my Mac G5.

The G5 PowerMacs run pretty hot, especially certain models. (You don't say which one you've got.) My G5 PowerMac displays temperature readings on the CPU similar to what you're showing there.

You can go to Energy settings in System Preferences and tell it to use less processor power (there are three settings, I forget the exact names, but they are something like Highest, Automatic, Lowest). Doing so will reduce the computing power of your machine but will also keep the chip from getting especially hot which will lessen the amount of fan noise from the computer.