The Fonts available have been added to recently so the information below is somewhat outdated. Look here for the announcement.
Here are the fonts available in Google Sites:
Normal - Normal/Serif - Courier New - Georgia - Trebuchet - Verdana
And here are different ones:
Comic Sans MS
So how do we use a different font in Google sites? First you should realize that fonts will appear on a viewer's screen only if they have that font installed on their computer. So if you install a special font in your computer and use it in your Website it probably won't look the same on everyone else's computer.
The six fonts listed above are quite commonly available on most Microsoft and Apple computers. Comic Sans MS and Impact are also quite common. In order to use them you have to edit the HTML and insert an inline style. Here is the code I used: