What are the best live chat solutions for websites?

You can go to SoftwareSuggest and see thier list of top Live chat software and then choose the best one for you. They also provide personal consulation and suggestions. You can also ask for free demo of any software. 

Currently I am using Lime Talk / www.limetalk.com. It's really good and doesn't cost a fortune.

There are number of solutions available for this purpose, you may try the following: -

~ Purechat.

~ Zopim Livechat.

~ LiveZilla

~ Stardevelop Live Chat (The best cost effective solution with multi-domain support, although with very limited features but cover basic requirement.

Regards

Irfan