I love cuckoo clocks. Always reminds me of my childhood. Yeah, as everyone has said there are both quartz and mechanical ones.
AFAIK, i remember I saw a quartz cuckoo clock which doesn't run on batteries but direct AC power via a adapter (something like your handphone charger). These type are more convenient, as you don't have to change the battery frequently, as mentioned by KimmJio, cuckoo clocks 'eats' batteries as it requires alot of power to run the cuckoo mechanism and the music.
As for mechanical ones, yeah saw that before too. Prices rather expensive though. There's an Orient boutique in Tokyo Street at Pavillion KL, saw alot of mechanical clocks there, if I remember correctly they had a 21 day mechanical clock too. I saw a few cuckoo clocks there but didn't ask whether it was mechanical or quartz.