I was going to use "iPhone" in the post title, but that would be a disservice to the alternatives available. It's no secret where my preference lies in the smartphone tribal war.
The smartphone is a computer with processing power and capability that far surpasses the most powerful PCs from only a few years ago. It's inconceivably more powerful than the computers that helped put men on the moon. It can communicate with people virtually anywhere on the face of our planet and it lives in your pocket.
As I've mentioned before, from the perspective of someone only a few decades ago these items deserve the 'Jobsian' buzz line "Magical".
While it's a leap to say that anyone has ever believed that a mobile phone of any kind operates actually by magic, it's easy to understand the sentiment. It's not it's raw computing power that makes it the best computer ever however. The utility of these devices is unparalleled. Smartphones came to prominence with the launch of the iPhone. There had been blackberries and Windows phones prior to this, but they were limited in function (though vastly outstripping conventional mobile phones) and had limited and often specialist third party application availability. RIM pioneered mobile exchange support and push email, but the limit of the handsets capabilities were still largely limited to those available when it shipped.
This was also the case with the original iPhone. Apps were an unplumbed depth, the phone had available only the software with which it shipped and Apple's early approach revolved around HTML5 and Java web-apps. We all know that this has changed somewhat.
So it was the evolution of the iPhone, closely followed by Android and BlackBerry from phone with extras to computer in your pocket that changed the world, relatively speaking. This opened up the smartphone to literally every task conceivable for a computer. Gaming, word processing, browsing, photography, satnav... there's almost nothing that these things aren't capable of.
This proliferation of fairly focused, small programs has also lead to a previously unseen level of integration. For example, I can use Reeder to browse through and read my RSS feeds. I can send select articles to my Instapaper reading list for offline reading later (which is automatically synced with my iPad) along with any webpages/articles or even long emails I may have received. From here I can post my favourite articles to Twitter for my friends to read, and via my Twitter feed I can push my friend's favourite articles to Instapaper as well. I have more methods to get in touch with people than I could ever really need; native social network support as well as access to pretty much all my media. All of these things, wirelessly connected, context and location sensitive (where appropriate) and small enough to fit in my pocket.
While other machines are more appropriate for certain tasks (there are some games that the restricted hardware could obviously never handle, significant word processing is easier and healthier on a full size keyboard and so on) the modern phone performs them admirably in it's way, and is always accessible. The best computers ever.