Your expectations of success
It's pretty safe to assume that most people don't set up a website so that it can just sit there like a bump on a log. You probably want your site to be active, have a lot of returning and new visitors, stand out from the rest, and maybe ( ok, probably ) make you a little money along the way. And while some sites seem to explode out of nowhere and roll off of everyone's tongue right away, you need to keep in mind that this happens to very few new websites. So know what your own expectations are, or your definition of "success", means before you start.
Do you think your site will be the next Facebook, Amazon or YouTube? Unless you are very unique, appeal to a majority of people, or improve on what is already out there, do not set yourself up for frustrations and a "What's wrong with my website?" attitude if you don't reach that level of success. All sites will have an appeal to a segment of the internet audience, but very few will create interest and "want" in huge numbers; it is based on what your site actually offers, and how many people would actually have a use for it.
Look at it this way: among the millions of websites online today, a very small percentage of them can generate the type of appeal to enough people that will make you enough money to buy a private island in the Caribbean. That's not saying your website won't be a success, or make you money if that is your intent. The point is that very few of them actually reach that level.
If you set a goal before you set up your website, and set benchmarks along the way of reaching that goal, you may be much happier with your progress as you see gradual, small successes along the way. So in essence, don't limit your success, but measure it as you progress.