I love Google Chrome on my desktop computer, and I also love Google Chrome on my Galaxy Nexus. Are those two facts related? Yes, yes they are.
Chrome is only in beta right now on Android, and it only currently works with (or, rather, it is only supported in) Android 4.0, aka Ice Cream Sandwich. But, for the most part, it does almost everything you need your mobile Web Browser to do, and a little bit more.
The big selling point to me is that Chrome on my phone interacts with Chrome on my desktop. Chrome on my Galaxy Nexus, for example, knows all my desktop bookmarks and browsing history. And Chrome on my phone will let me open tabs I just closed on my desktop. It's beautiful synergy.
And that, ultimately, is why you would want to use Chrome on your phone. It makes the transition from sitting at home to on-the-go quite seamless and wonderful.
And then there are the cool little perks, like the ability to swipe between tabs without ever going to the tabs menu. And the way you can open up an incognito tab, to let you browse without leaving a record, just like you would on your desktop to look up... well, you know what you would look up when you're incognito.
The downside, of course, is that Flash is not currently supported in the beta version of Chrome. But that should change when the browser gets a full release in the next month or so, so I'm not worried too much about that.
What really matters, though, is that Chrome interacts with all the other places you have Chrome installed, and that's just great. It simply makes life that much easier.