I considered an extended battery, but I prefer to use one of these.
http://www.amazon.co.uk/5600mAh-Exte...7481517&sr=1-3
It gives me well over two charges with the phone switched off, but you can have the phone switched on obviously. That means three full charges if you leave with a fully charged handset.
While it does involve having to connect via USB, I don't find it a problem. If you have to make a phone call then you can charge sufficiently to do that pretty quickly. In any case, with a short micro USB cable you can hold both the phone and battery in one hand easily, if it's ever necessary - although I've only had to do it once.
This model (5600mAh) is very light and I hardly notice it in a pocket - in fact I doubt I'd notice another one either. For that reason I've been considering buying more.There are larger (and smaller) versions for those who need more power, but the thing about having two is that you can distribute the weight and bulk. Having two lighter batteries in different pockets seems preferable to me than having one larger battery in one pocket that is more noticeably heavy. However the bigger versions do allow charging of two items simultaneously, or one item more quickly - I guess that might be useful to some people,
That is also why I prefer this solution to extended replacement batteries. I find it preferable to keep the slim and light profile of the S3 and have extra power if I need it, rather than being permanently saddled with the extra bulk of the replacement battery, when in reality there are many times I won't need it.
There's also the bonus that you can charge anything else that can be charged via USB - other phones, laptops, ipods etc. There's even a handy flashlight function as well!
Having owned one for a month or so, I fully recommend it.