Now Chrome for Android is out of beta, which means that it should be more stable and more reliable. For some reason, the Chrome mobile app is not in sync with the desktop app, so the latest stable version is 18.0.1025.166, which corresponds to the desktop versions from April.
I've been using this browser since March, when I was able to install Android 4.0 on my Galaxy S2 (Chrome requires Android 4.0). It's really fast, the deck-of-cards interface is intuitive, you can open as many tabs as you want and the browser saves the list of tabs and even the part of the page where you stopped reading. Other than the lack of Flash support, my main complaints are that Chrome for Android uses a lot of resources (internal storage, RAM, battery) and there's an annoying gesture that conflicts with horizontal scrolling. You can "swipe from the right edge of the screen to the left to go to the next tab in the list," but the same gesture can also be used for scrolling.
Chrome for Android is the default browser for the Nexus 7 tablet and probably all the future Nexus devices will include it. Chrome replaces the old "Browser" app and the most important thing is that Chrome will constantly be updated, since it's a regular app from Google Play.
It will be interesting to see if Android OEMs will bundle the Chrome app or continue to develop their own browsers. Even if your new Android phone or tablet will have a different browser, you can always install Chrome from Google Play. Unlike iOS, Android lets you set a default browser and you can even disable the bundled browser.