Using the iPad powered by the mains good or bad?

You will get opinions both ways I'm sure. I use the iPad both ways - while it is plugged in and when it runs strictly off the battery.

I use my iPad all day at work - on battery power only. It is set for auto-lock after 5 minutes - so it will sleep after 5 minutes of inactivity. I leave it turned on for about 12 hours each day like this - battery only.

When I get home, after dinner, I plug into the power adapter and charge it. I continue to use it and I let it charge all night. Then I repeat the process all over again the next day.

I would not recommend using it constantly while it is plugged in and that would defeat the purpose of the portable nature of the device anyway. Once a month I let the battery run all the way down until the iPad shuts off on it's own as Apple recommends. Then I plug it in and let it fully recharge to 100%.

Here is Apple's take on the iPad battery

http://www.apple.com/batteries/ipad.html

You can run it any way you like. Just make sure you run it on battery every once in a while. It is not very handly plugged into the mains though. I plug it in whenever I have a chance, or gets anywhere below 50%.

Battery is good for between 750 and 1000 cycles, and a cycle is a full charge from empty. Two charges from 50% would only equal 1 cycle.