The basic restrictions are CPU usage, memory usage, and inode usage. If you consume more resources than you are allowed to, you might get a temporary ban on your account. Fortunately, for most reputable web hosting companies like Hostgator, their basic web hosting packages are already quite sufficient to the average users. If you aren't using any buggy script and you are running your site in a normal white hat way, you would seldom or most likely never overuse the allowed limits.
The only thing you might have to check is the number of files you are storing. Each file requires one inode. If you are getting more websites or blogs, that means you will be having more files, then you might need to upgrade your web hosting package. For the best unlimited web hosting service, I would highly recommend Hostgator. I did try other web hosting companies in the past, here is a post about why I still use Hostgator.
