Your kids ears are still developing and can be damaged by harsh noise.
How much do you value your childs hearing?
You need to ask some questions
1 Do you want ear bud style?
2 Do you want ear canal style ( thesae use a silcone rubber tip which presses gently to the first bend of the ear canal
3 Do you want on ear Style
4 Do you want over ear style
5 Lastly, do you want open back ( leaks noise in and out..which means that if the kids use them in a noisy enviroment , bus, trian, plane, sitting room with the TV on, they will compensate by turning up the volume of the player. or do you want closed back that allows much less noise to be leaked in and out.
Closed back generally means that your kids will not have to turn up the volume to compensate for external noise. It also means that you can sit next to them in the car and not hear the whizz ding noises
I would not recommend 1, they can be uncomfortable and kids tend to ramp up the volume too much.
I would go with 2, 3 and 4 in closed back version.
Sennheiser HD201 closed back, over ear
http://www.amazon.com/Sennheiser-HD...1?ie=UTF8&s=electronics&qid=1226828462&sr=8-1
Sennheiser HD202, closed back, on ear
http://www.amazon.com/Sennheiser-HD...1?ie=UTF8&s=electronics&qid=1226828520&sr=8-1
JVC marshmallows, closed back, ear canal
http://www.amazon.com/JVC-HAFX33A-M...1?ie=UTF8&s=electronics&qid=1226828687&sr=1-1
Any closed back type by a major supplier such as
Sony V150, closed back, on ear
http://www.amazon.com/Sony-MDR-V150...1?ie=UTF8&s=electronics&qid=1226830374&sr=1-1
Panasonic
Sennheiser
Denon
Kos, closed back over ear
http://www.amazon.com/Koss-20-UR-20...?ie=UTF8&s=electronics&qid=1226829105&sr=1-20
Beyerdynamic
Audiotechnica, closed back, on ear
http://www.amazon.com/TECHNICA-ATH-...3?ie=UTF8&s=electronics&qid=1226828831&sr=1-3
happy hunting
Final edit
All the ones linked above should work ok with the weak amplifier circuits in ipods and Nintendo DS. The harsh top end should be kept controlled and there should be some nice bass for music. I have listened to many of the examples listed and they sound very good for the money. I would be happy to listen to them on a plane flight. We have 18 pairs of headphones here between us, some costing as much as $300
