My son leaves his device on all the time and tells me not to turn it off. Is this o.k., or should it be turned off when he's not playing?

you can put it in sleep mood

I leave mine on all the time. As long as the lids shut when its not used it puts it in sleep mode and doesnt drain as much power. Its can be left on so it can pick up streetpass/spotpass/updates etc

Depends on which DS you're talking about. The 3DS should be on at all times to receive wireless info while in sleep mode. The DSi, DS Lite, and DS Phat (the original brick one) can be on, your game will pause until you open it again. If you're not going to be playing it for long periods of time though, it's best to just turn it off and save the battery. It only takes a few seconds to start up the games anyway.

It can't hurt much, but it's a waste of electricity.

Well, if you want to waste energy, wear out the re-chargable battery, and deal w/ the annoying blinking light, be my guest. Yeah, re-chargable batteries stop working after so many charges. Once, I came over to my little cousin's house to "fix" his DSi (he always left his on all day, until that day, that is). It wound up, the battery died. Go figure. I leave my 3DS in sleep mode a lot, but the battery slowly drains and it's a waste of energy after so long. You decide.