So computing power generates bitcoins? Is it ethical for me to use the 3 8-core machines at work I have to generate bitcoins for my personal use? What about my personal work machine?
No. There's a constant average rate of new Bitcoins created, and that amount
is divided among the nodes by the CPU power they use. When Bitcoins start
having real exchange value, the competition for coin creation will drive the
price of electricity needed for generating a coin close to the value of the
coin, so the profit margin won't be that huge. The easier way to gain a lot
of wealth would be trading goods.
At the moment, though, you can generate new coins quite profitably, if you
expect them to have real value in the future. If you choose to, be aware that
Bitcoin is still experimental software.
It seems like it would be a lot easier to simply trade for bitcoins.
That depends on who you are, and what kind of value you can get out of bitcoins. ;)