Many novice web-designers like the idea of a unique, sometimes Cursive font. But using cursive fonts may be bad for readability, and may end up harming your site. Younger People are not as used to cursive fonts as their parents, and many can't even read cursive fonts. Obviously some fonts will be easier to read then others, but the closer it comes to handwritten text in cursive, the harder it also gets.
Cursive fonts are best used on sites where you aim to get a certain theme. Like on music and movie sites, where the font is used to create a certain feel to the site, and on sites where users normally won't spend a lot of their time reading.
There are many pretty cursive fonts, which may give your site a push towards your design goal. Whether its just to give a nicer look and feel, or part of a bigger marketing plan for your website.
Where to find cursive fonts
The best places to find fonts, are likely on sites specialized in providing fonts with free licenses. When you have found a font that you would like to use, be sure to read about the @font-face rule in CSS, which allows you to embed your fonts, without having to resort to crazy stuff, like replacing the letters with images on the server-side. Some of the free font sites would include the below.
Not all fonts are free, so if you find a font that you really like, then there's nothing wrong in buying a license. Just be careful to read the license terms, since some don't allow you to use the font for everything that you might intend.