My 5 year old DD got one at Christmas and it is the best thing since sliced bread.
I think a lot of the objections people raise are quite superficial / inaccurate complaints tbh...
It's too expensive - not necessarily, ours cost £50 for a second hand, 2nd generation one and that came with a set of speakers. This was about half the cost of the sylvanian families house that she also wanted. Even a full cost one is no more expensive than a bike, Nintendo DS, Sylvanian families regency hotel + 1 animal set, a Barbie's doll's house, a trampoline...
They should be out playing proper games - that's a false dichotomy. Having one does not stop them doing proper games. It depends on what rules you establish. We have a 'not in the house' policy. So I tend to keep it out of reach in the house - so they mostly use them when they're stuck in confined spaces such as when DD has to sit quietly (and still) for 3 hours at a gymnastics competition. Then they're a godsend. Also, to be fair my DDs wouldn't choose to play with them when they've got a dolls house, dressing up etc to play with...
They get broken easily -Not necessarily. You can buy cases which will cover all the sides except the screen. This will give a lot of protection and will cover dropping them from adult waist height onto a tiled floor - trust me I've dropped my iphone and the case has been great protection! ... Or you can just do as I do and teach your children to respect their property! At 5 my DD is responsible enough to know that this is an expensive toy and she musn't leave it lying around, or throw it etc. She's had hers for 6 months without a problem.
Next year you'll have to buy an even more expensive present - err, why? Two years ago, my eldest daughter wanted an ipod. We bought her a second hand one. The following year she wanted hair curlers. So we bought her those. They cost £25 and that was her main present and she was thrilled with them. This year she wanted a hamster. That only cost £8! (and it is the present that she reports to be her very best present yet). My daughter's presents have actually been getting cheaper as she has been getting older. In fact, the most expensive present either of them have ever been given was a dolls house.
They'll go on the internet with them - no, not necessarily. They need wifi to go on the internet. If your neighbours have locked down their internet (like mine have), don't give them access and they can't! Besides my DD hasn't actually worked out how to use the internet on it yet, because I haven't shown her how!
There's no point to them without the internet - yes there is. I download the apps through the app store and then sync the phones to them. Same with the DVDS. My DD2 thoroughly enjoy hers without accessing the internet. There's tons of apps you can use without the internet.