The most interesting thing about websites to me is how much personality you can put into them. That makes it fun for almost everyone--especially the website owner.
A good website is long on content and that just screams for personality. Speak from your heart; your mind; your inner child. You get to choose. In fact, I think it is the personality that makes the site. We could call it flavor. You can be real or a little wild and crazy. It all works extremely well in the website. Here's a fun site (and very effective): Juggle Now. Here's one that is in need of a personality: Juggling. The difference should be obvious and dramatic. I choose fun.
Here's another fun place: Threadless, along with one owned by the same company: Extra Tasty. Here's a fun one that we built: Wine & Spirits World. It is perfectly okay that everyone on the planet may not like it. If you are being yourself and flowing with that, it will be good. You will have a better and more effective site.
Keep your objective in mind. What are you trying to achieve with your website? If you are selling things like an e-commerce site, personality is just fine while you keep your vision on the end result of making sales. If it is an informational site, you can have lots of fun with information.
You can also add a blog like this one and add some of your personal philosophy, thoughts and feelings. Some might keep there website more business-like and have their blog be the fun thing. That's cool. There is nothing wrong with making them both fun.
Your website needs to be constantly evolving and becoming more and more effective, useful and fun. Keep your site evolving and becoming.