I have a site on its own domain hosted by a web hosting service company. Will my IP-address ever change? Ever? Or will it be the same for ever?
I assume its an all-in-one package you have with one company and I assume the IP address you refer to is in connection with the domain.
Generally, the IP address should stay the same unless some company in connection with your hosting company decides to make some changes involving IP addresses, but the odds of that should be very low, especially if the company is reputable.
If you want more control, you can own (aka rent yearly) a domain name from a registrar and hook it up to a dedicated server box which comes with an IP address. By hooking it up, I mean setting the IP address in your domain name registrar control panel to that of your dedicated server box.
Such setup is expected to take between 1 and 48 hours for the whole internet to understand the mapping of the new domain.
Regardless of what setup you take, Just make sure you are notified by the host in advance if your IP address of the computer your domain is connected to changes. The only way the companies should not have to notify you is if you fail to pay your bill and/or breach the terms and conditions set by your web services provider(s).