What is the purpose of your website? Most of the time it is to enlighten your clients about your products and services.
Legible and professional-looking fonts are going to make this an easier process. If your clients have to decipher the fancy or cute-looking fonts and it takes them longer than 5-10 seconds and it gives them a headache I bet they won’t stick around.
Just by looking at the font you can tell if it’s a professional site or not. You might think using Comic Sans makes your site look friendly but in most cases it really just makes it look like a homemade website.
Also, many times your cute, creative font is not web safe which means that not all users have that font installed on their computer. Therefore their browser will default to a basic font, leaving your site looking horrible.
So, stick to a simple web-safe font like Arial or Verdana and get the message across instead of trying to make your website cute.
Your website is a tool to generate more income and not to express your inner creativity.