Perhaps they are available everywhere and I haven't noticed, but in Japan they have cellphones with 4 programmable buttons on them. You can't call anybody other than those 4 people. They are quite popular as emergency cell phones for children and the elderly (the latter because the buttons are really easy to push).
I met an one of the entrepreneurs behind the jitterbug(now known as a different company). Initially they focused it at parents wanting phones for their children, but now it's mostly for the elderly.
He said they failed at their market research - they tried to make something that appealed to parents, but neglected to see what kids actually wanted(to have things like the adults do). American kids knew it wasn't a real phone, and rejected it. Their parents then got them a flip phone instead of a "kiddie phone".