If you don't know who your site's biggest fan is, then you're probably in the wrong line of work.
Think about it.
Who spends the most time viewing every single detail of every page? Who keeps up with and checks over every update? Who's right there noticing every color choice, coding change, style effect, and anything else that has to do with your site? That's right, it's you.
If you're not your own site's biggest fan...
If you're not your site's strongest advocate...
If you're not excited by nearly every new feature you add...
Well, then, who will be? If your site doesn't thrill you, then why should it interest me or any other user? In fact, if your own site doesn't excite you, then you're probably a bigger detriment to it than a help.
You're the one that has to sell this thing to its intended audience.
Promotion of your site must begin with you, and you should start with the people you've already sold it to, your own clients.
Make announcements of new features.
Get input from every department on how the website can help with their specific goals.
Be excited when you talk about it, and get them excited too.
You're the site's biggest fan.
Let everyone know why they should be a fan too.