(Update after 2 weeks is below)
What is it?In case you have not seen it, the Moto 360 is a smart watch that is paired with your phone. It is far from the first smart watch, but it is the first watch that I thought was good enough to buy. A big part of "good enough" is that it looks like a real watch, being round, and it looks great.
How I use itMostly I use it as a second display for my phone. It is much easier to see a notification on my watch than it is to pull out my phone and see what just came in. The most useful alerts are text messages. I have also gotten a bunch of Facebook messages and call notifications. There is a setting to ignore messages from certain apps that I have configured for games, LinkedIn and WiFi notifications.
You can reject or answer calls from the watch. If you answer the call and are on a Bluetooth headset you can start talking right away. If your phone is needed, you still have to pull it out of your pocket. I have a Bluetooth speaker and mic in my ski helmet, so I think this will be a very useful feature while skiing.
Google Now provides alerts for many of my interests. It will display the SF Giants score as it is happening (configurable for spoilers), tell me when I need to leave to drive to an appointment and other interesting news and event.
Other great usesI have set up my watch to alert me if I leave my phone somewhere. Whenever I walk more than 20-30 feet from my phone, my watch alerts me to it. I'm using Wear Aware.
My phone unlocks automatically when I am near it. I set up my watch as a trusted device so that I can skip the lock screen or fingerprint reader. The phone locks automatically if I leave it somewhere. Try this or this.