No, not really trust to luck... absolutely nothing is hacker proof although there are hordes of software companies and open source groups working to make it happen... you get one security hole patched, hackers just look for another... it's a bit like a game but with serious consequences. However, the normal worries of hacker issues are usually covered by your hosting service. Your hosting service will have a list somewhere on their site what they protect against, even to email virus scanning. If they aren't keeping secure servers, it's time to look for another. The typical hacker who does damage to websites is not really a hacker in my book. He is a kid( whatever his chronological age) with too much time on his hands who found some scripts to use against an insecure web server. He defaces websites because it gives him a sense of power and it's not too hard to do. If it's hard, he moves on until he finds one that's easy pickings. So, if your host is good, you can sleep fairly easy. For a hacker to work very hard to crack open a server there has to be something there he wants bad enough to work for it.
Other issues, such as the ones I mentioned above can be handled usually through keeping the web applications you use updated because security patches are frequent. However, they are not typically your hosting service's responsibility to guard against even if they offer those apps through control panels such cpanel with fantastico, ensim with power tools, and so on.