My previous provider used eSupport Suite, it seemed to be okay. It has a knowledge base, file downloads, live chat and support tickets to name a few. I believe it also has a FAQ or something close to that.
There is quite a variety of free and commercial live support centres. I can't remember the name of the free one, although a quick search on HotScripts should find it. In regards to commercial ones, a few decent include: Kayako and ProvideSupport.
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I agree with you monaghan, I do not use a live chat system but have support tickets available and have not had a problem with customers complaining about not being able to contact us 24/7. Sometimes we can use an IM client at the customers request to have a live chat if it is needed.
24/7 is available for premium customers, We just don't offer it as standard on the budget packages. If someone's that concerned with having 24/7 support then why on earth do they host on a budget package
Of course, it's all about knowing your customer and then setting & meeting their expectations. I have a consultancy customer in New Zealand we we "meet" late night or early morning. Others in the USA have a longer overlap. I have thought about an outsourced helpdesk in other time zones, but (fortunately) my current customers don't generate sufficient support requests to justify it.
I provide support for many corporate helpdesk systems (software & database), I've seen so many systems simply neglect the fact that they could resolve most complaints by simply setting the customer expectation in the 1st place
For support tickets/FAQ I use Smarter Ticket. Seems to do everything I need it to. The only live chat system I've used is Crafty Syntax. Again, does everything I need it to. I also think MSN messenger is brilliant for live chat. It may look unprofessional to some, but it's there and free, so why not use it? I haven't had any complaints about it. Some customers prefer it.
A number of our clients use MSN and like to contact us through there. The only thing I would recommend with MSN is to make sure you have someone available at the hours specified, if not then use it when the client requests it. Some support tickets are far easier with real time responses.