tawk.to

Tawk.to offer all the features you can need with a live chat to provide support or to talk with your visitors, and there is no hidden fees or anything else.

Everything's unlimited. Beautiful interface. Everything's free!

It's free (and, yes, it's very important for me) and very useful!

Its great, we use it at work to talk to our clients.

This is the best alternative to Zendesk.
I wanted to get rid of the non-paying-customer-annoyer-chat-badge.
Tawk.to does everything that the free Zendesk app does, but also alot more. No restriction of chat agents amount.

Only bad thing is that you cannot choose the color. But you can choose a bubble, it is a strange icon next to the chat button and there is a huge choice of those, in many, different colors. Just choose one that is about the same as your brand color and then click the option that the chat widget will use bubble colors. Then just disable the bubble and the color stays. That is important, because without my own color I would have chosen the annoying but colorable Zendesk. Or something else.

There is also branding on free version, its a small text: "We're (then a thunder bolt, that is supposed to symbolise "powered" or smth.) by tawk.to"
Nice and tasteful, I would include that, even if it was optional, just for the free chat, its more than ok.

Compared to Zendesk, Tawk.to can also show logged in members names and also shows a flag of the country that the customer appears in. I also love whispering between agents, etc.
To come to think of that now, I was using Zendesk and was quite happy with that, little did I know...