Does Android support new fonts?
Yes, you can install new fonts, but it requires root on most devices.

To install a font, you just simply need to copy the font file (.ttf format only) into /system/fonts.  There are also numerous apps available on the Play store to do this automatically for you, such as the plainly named Font Installer.  Other apps also include functionality to find new fonts.

With the right app, it is also possible to install fonts without root on the Samsung Galaxy S3, S4, Note, and Note 2.