If your talking the wii, i wouldn't even leave it on 24/7 in standby. There's a severe design flaw imo, where it will just get hotter and hotter as the fan doesn't kick in when its left in this mode.
Although there was a firmware update (I believe that might address this) which was released after I sold mine to a dodgy scam shop in leeds (revenge!), my GPU actually broke in my wii due to me using wii connect 24.
Apparently its a 'broken batch', but its soured me off of Nintendo hardware standards.
http://www.vgchartz.com/forum/thread.php?id=4310The real problem is I had absolutely no reason to turn it on again after beating Zelda, so that was kind of the problem.
If you mean leave it on completely, then the fan will be running... make sure its extremely well ventilated. However, my launch unit overheated without it being turned up for long durations, just in standbye.