For anyone recommending Zopim, I recommend you to read about this nice little proof of concept that allows me or anyone to impersonate anyone in your live chat. So you probably should not use it for private area chats or anything remotely significant.
PS, most of the live chat widgets suffer from this issue. Perhaps something to be addressed...
We are using crisp.im and finding it pretty great for several reasons:
1. The free option gives you upto 2 operators (most others give only 1)
2. The mobile works pretty well, so you can provide support when you are on the road
3. The dashboard is clean and clear
4. The paid option has several cool features if you later want to pay for it