The only passenger rail service in the country is on the recently rebuilt Panama Canal Railway [1], which runs between Corozal, a few minutes’ drive north of downtown Panama City [2], and Colón [3].
Some Panamanian businesspeople use it as a commuter service, but for most travelers it’s a day excursion, and getting there is all the fun.
Links:
[1] http://www.moon.com/destinations/panama/panama-canal/the-former-canal-zone/sights/panama-railway
[2] http://www.moon.com/destinations/panama/panama-city
[3] http://www.moon.com/destinations/panama/panama-canal/colon