I would call it the Age of Communication. Every other person you encounter has a cell phone. The next time you're driving somewhere, pay attention to how many people talk on the phone while driving. Consider how popular Facebook and Twitter have become. They're more for communicating with other people than for spreading information. With a satellite phone, there's no place on earth you can go and not be able to call somebody.
I will go with "Information Age". Just like the stone, bronze, industrial, etc. ages, the information age is the defining technological and societal change that is still sweeping the world.
What about "the age of technology?" I'm just trying to think of something that encompasses all the changes we've experienced in the last twenty years or so. It's really amazing. In one of my first years of teaching (which wasn't THAT long ago...at least not to me!) I took a class on using a dial-up modem to access something called a "bulletin board." I thought the class was such a waste of time...after all, no one was using "bulletin boards" and how could such a thing ever be useful to me??? Wow. How things have changed!
I think it might be referred to as a Digital Age. Like many posts above, our era is certainly defined by the technology that represents us. One complication that this has presented is our over-reliance on technology... I wonder what global chaos will ensue if the internet crashes and massive pieces of information are lost. We are extremely dependent and I wonder what the age will be referred to after a significant tragedy.
If it's like many other generations before us, the octogenarians of the era will probably call it "the good old days." Life seems to get more complicated as technology advances, and the early 21st century will probably seem like a quaint time of life a hundred years from now.
It sounds a little cliche, but I'd have to agree that this time period in our history will be referred to as the information age, given how our access to technology and instantaneous information and personal communications devices has exploded over the last generation, and how that has affected many, many aspects of our daily lives - education, the workday, entertainment, interpersonal relationships, etc.
That's very hard to guess. I would say that my first guess is that they might remember this as the "Early Internet Age" or "Early Globalization Age." I suppose also that this depends on what country you are living in. I live in the US and so that of course colors my thinking.
I think that the globalization of the economy, which is being rushed along by the internet and computers, is likely to be a huge change in the world. I think it is likely to have an impact somewhat similar (maybe not as much, but who knows) to that of the Industrial Revolution.
It's an interesting as well as a tough-to-guess question. I think, as the world is experiencing conflicts among different countries regarding nuclear power in this 21st century, the next century would be a a post Third World War period, or post-nuclear age, since, I think humans will be able to discover something new and more destructive than nuclear power after hundred years.
The most widespread and far reaching development of the current period which, perhaps started around 1950, but which became very in last two or three decades is the rapid and major developments that have taken place in the area of information technology (IT). These development in IT include major breakthrough in technology as well as widespread use of this technology. These developments in IT are still continuing and likely to be continue for some more time to come. Because of these changes the current phenomenon we are going through has already is widely referred to as Information. I believe any major developments or to exceed the scale and importance is likely to take some time. Thus, I believe, people living a hounded years from now will call our age as the age of Information Revolution.