What countries can green card holder can travel without a visa?

Answer 1

USA, Canada, Mexico, some Central American countries, some Caribbean islands, Switzerland. and to those to which nationals of your countries are allowed to travel without a visa or resident permit. There might be some more. Note: You must hold the actual card in most cases.

Starting Dec 2008, Switzerland is a part of Shenghen nations and does not waive visa requirements for GC holders.

Answer 2

To be honest it depends on where you are from and what country has granted you a green card. US green card holders can visit Mexico and Canada without a visa, but you still need a passport and leaving the Us for over a year can lead to having your green card taken away.