Fonts are lots of fun to play with. Where you can get into trouble with them, however, is when you use a non-standard font on your website. Why? Because if you use a font that is not SUPER common, it's quite likely there will be people who look at your site that don't have that font on their computer. What happens then? It defaults to times new roman if you haven't chosen any other fonts to default to. Why is that a problem? For me it's a problem because I like to have a pretty good idea how my sites are going to look for most people .
It is very possible that is because I am a control freak perfectionist and I am not a fan of Times New Roman.
It is helpful to choose a list of fonts so that if your first one is unavailable the page defaults to the second, then the third, etc. Try to choose at least one common (arial, veranda, geneva, etc.) font so that your page will get to that one if nothing else works.
If you are creating your own html, you can use coding similar to this: <FONT FACE="Arial, Helvetica, Geneva" >. (This means if arial isn't available, helvetica will be used, if helvetica is not available it will be geneva, if geneva is unavailable it will default to times new roman).
If you are using a designer, they will probably already do this for you, but it won't hurt to send them a list of fonts that you like to work with.
When I use a "fancy" font (one many people may not have), I tend to use it for titles or emphasis only, and usually create a photo of the title rather than adding it as text . This allows me to control what the page looks like and still use my chosen font. Otherwise, the result can be this:

Take care!
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