In the olden days, there were only about 7 websafe fonts. This was because in order for a visitor to your site to see the font you used on your site, it had to reside on the device they were using. Thanks to google fonts, there is a free option to let you pick from hundreds of fonts. The fonts are stored with google so you don’t need to have it and neither does the visitor.
Any drawbacks … afraid so. This may slow your site down slightly. Check google analytics ( http://support.google.com/analytics/bin/answer.py?hl=en&answer=1205784 ) to see how quickly your site downloads before you change it and then check it again after to be sure it isn’t a huge drain.
If your site is using a style sheet, the change to a new font is easy! If it does not, then it may take a little longer to incorporate the change, but shouldn’t be too bad. If this is something you wish to do to change the look of your site, just let us know.