Well the BabySitting Mama for the Wii is just one of those things! (scroll down to the bottom of the feature at Dealspwn at the end of the link for their take on it)
Basically, you get a life-sized doll baby thing which you put the Wii remote into and then you have to look after this baby, which reacts to movement and motion, from the moment it wakes up (well, when you put the disc into the Wii and switch it on anyway) until it closes its eyes at the end of the night.
Apparently tasks like changing nappies are included in the BabySitting Mama tasks - I wonder if there's a virtual naughty step too...?
Actually, I can think of something worse...the time when I had to babysit my dad's Tamagotchi when he took my mum away on a cruise and she refused to let him take it with them (don't ask, he's a scarily clever F1 engineer in his sane life!).