someone has asked me a question that which one is best but i am not able to justify as many time we have seen that godaddy sever has gone down and many times same things happened with hostgator.
Your post is a bit ambiguous. In the title you ask about customer support, but then you go on to talk about server down-time, which is not the same thing.
Do you want to know which company provides the more reliable service, in terms of server uptime? Or do you want to know which company's customer support is better - i.e. more helpful and efficient at dealing with queries and resolving problems?
Also--keep in mind that godaddy is not a true webhost. Their primary business is being a domain registrar. Anything else is just a side business (and thus, doesn't have their full attention and dedication).
Are you looking for registrar and/or hosting recommendations?
Any hosting provider can experience downtime, the ones with the best customer support deal with these issues promptly, and keep their customers informed while doing so. Between the two companies you mention it looks like only Hostgator has a Service Level Agreement for shared hosting, so based on that I would say Hostgator would be the better choice between the two for basic website hosting.
GoDaddy is a very popular registrar, you'll probably do ok if you choose them for your domain registration.
Yes, I also believe that for domain registration godaddy is the good choice, but not for the hosting.
I have been using GD for quite some time now and have been pleasantly surprised by their support. Hosting might not be their core business but overall performance is good. Also its a personal experience because some have had good experience with GD while some have had good experience with HostGator. Also if I am not wrong GD has servers in multiple locations like US, AP and India so you could select a server closest to you given your location plus they have call centres in these locations too.
Always avoid GoDaddy for web hosting. Their core focus is on selling domain.
But I prefer 1&1 for web hosting.
As the OP hasn't returned to explain exactly what they want, I think it's time to close this thread.
Thanks to all who contributed.