I always turn them off if I'm not planning on playing for longer than a half hour or so.
I turn mine off especially the 360. Don't want to do anything that would contribute to the ring of death.
Why So Serious?
I always turn off my consoles after use, but if I have to eat or get distracted, I may leave it on for an extra hour but not anymore than that. I think the longest time I ever had a console on was when I left my NES on over-night since I couldn't save in Super Mario Bros 3.
I never have anything turned on if I'm not using it, save for one computer.
Actually, even with the red power light, the Wii is still in standby mode. The only way to truly turn it off is to unplug it or turn off the power strip if it's connected to one.
That goes for all electronic devices that use a wireless remote controller (Wii, TV, DVD player, VCR, etc.). "Off" is never truly off. That's why the power buttons on modern electronics stay lit, even after turning them "off." It's to show that the device is still drawing power:
Wikipedia - standby power
"Standby power is typically 10 to 15 watts per device, and occasionally more. ... Although the power needed for functions like displays, indicators, and remote control functions is relatively small, the fact that the devices are continuously plugged in, and the number of such devices in the average household means that the energy usage can reach up to 22 percent of all appliance consumption, and around 10 percent of total residential consumption. ...
Alan Meier, a staff scientist at the Lawrence Berkeley National Laboratory (LBNL) in Berkeley, noted that many household appliances are never fully switched off, but spend most of the time in a standby mode. His 1998 study estimated that standby power consumption accounted for...more than $3 billion in annual energy costs.
According to America's Department of Energy...the wasted energy is equivalent to the output of 18 typical power stations."
Turn off your power strips before you leave for work and before you go to bed.