first of all I'm new in this area and I hope it is not a very stupid question.
There are a lot of server center in the world, but if I want my own webserver, how important the location of the server is?
I mean is it important to be in the same town/area to make a personal visit or it can be on the other part of the continent (if speed, stability,... are the same)?
Is there any company who never see their own servers?
It really all depends. If you actually own the hardware and you are just colocating your server in a datacenter, you may want to be accessible to it as the majority of the datacenter do not provide technical support or hardware replacement in that situation. So being near would allow you to drive down to the datacenter and replace a damaged component.
Also since you are putting an expensive hardware, it is good to know who you are dealing with. Anyone can say anything about themselves but a visit can tell you quite a lot about the business. At least you will know if it is a legit setup and not something set up in a basement of a house.
Of course if you are not actually using specialized hardware configuration then like most of us, we just rent a server from the datacenter. By getting a dedicated server, you do not need to worry about hardware component replacement since that is the datacenter's issue. This way you do not need to worry about losing your hardware and you could 'upgrade' or terminate your contract any time. For some reason, it is usually cheaper to get a dedicated server as opposed to a colocated server.
And some of the companies are so kind as to send you picture of your server. When you worship a thing it positively serves better. This is a proved religious practice. With the nowaday's managed services you never know.
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I never see my servers nor visited the DC, the company, the sales staff or the support staffs, and I have been providing services from my servers for more than 2 years. I am in SG and I rent servers in US. BTW I'll only rent servers from US, as of now this is the only country I trust I will get what they said or put on contract. This is the age of Internet, we surf the world with our PC and talk with our fingers, without moving our butt a bit.
Yes in SG (Singapore) we don't see downtime like what I see in US DC. In fact my server in SG has zero downtime so far. Because SG is small thus the DC is never full, so no overloading. Yes SG is more expensive generally. Using US servers is to serve the world. Now all my clients are in SG and Asia, furthest away is London. Some clients still stay with us even they move from SG to London. It is a business decision to rent US server. US is very well connected to the rest of the world and can be trusted as I said before. To reach to the world, I must make sure the world can reach me or my server via Internet.
Prerequisite to do what I do, learn how to manage your server/s remotely.