Is it better to turn the computer off or put it in a sleep mode when not using it?

Shut everything off, an don't forget to disconnect the power going to transformers and adapters because they use power even with the devices shut down. They only exception I know of is that your cable ISP may want you to keep your modem on so it can receive firmware updates.

Powering on and off will cause more wear & tear to the moving parts if your system has any (HD, fans etc.) Also, if you do plan to turn the system off, leave it doing nothing for a few mins before you do to allow the fans to remove any latent heat, as this hanging around inside a PC case will cause more harm than good.

It depends. If you're not going to use it for an extended period of time, such as when you're sleeping, I'd turn it off if I were you.

Its debateable... If it will be ignored completely for an hour or more, you turn it off, otherwise (for about half an hour or less) sleep mode is fine.

Don't forget also about the money you are spending in power being supplied while you are not using it...