Mobile phones are used by almost all of the people, every day thousands of phones are activated throughout the world, and they bring everything to satisfy the final customer: internet, camera, gps, etc...
Now to buy a mobile, we have a lot of things to choose from: model, size, color, operating system. Even we don't pay much attention to its main function, the function that really matters: calling.
With flat rates, we all read the news online, check mail, chat, etc… All this with mobile phones.
The phones have had a great growth, previously we only used them for to its main function, now we use them for that and more, helping us a lot in our daily lives. We no longer rely on computers to be on the internet, but of course, computers are better, faster and more comfortable, but mobile phones are not far behind. Engineers work in pretty big companies on how to improve these characterizations and to make them more attractive to the final user. All this to make life more comfortable, but still we should not rely heavily on them; we must also learn to control our use of them, use them for what really matters.
Is it indispensable? No. It is useful, yes, but we can live without them.
Summarizing: the phones are very useful and we make things easier, but we shouldn't depend on its use.