Anything that was originally done with harmony works - all Everly Brothers songs, for example.
For Country, I usually use one additional voice a third above my own, with the harmony voice a little softer. This actually will work for any genre.
On some old songs, such as Mills Brothers, additional voices can be used the same volume as the lead voice.
A good idea would be to listen to recordings of the songs you do to see where the harmony originally was used. However, feel free to make the song your own arrangement.
It's easy to overuse the harmony. Like seasoning food, be discreet and use it sparingly for best results.
DonM