In the United States, the state flag with a predominantly green background is the flag of Washington. The flag features a dark green field with the state seal in the center. The seal displays a profile of George Washington, the first President of the United States, and includes 13 stars representing the original colonies.

The flag was officially adopted in 1967, although variations of the design have been used since the late 19th century. The green color symbolizes the state’s lush forests and rich natural resources, reflecting Washington's identity as the Evergreen State.

Another example of a state flag with green elements is the flag of Oregon. While Oregon's flag has a blue field, it features a green design on the reverse side, which is unique among U.S. state flags. The reverse side showcases the state seal with a representation of a beaver, the state animal, which is often depicted in shades of green.

In addition to state flags, green is also a common color in various territorial flags and city flags across the United States. For example, the flag of New Mexico incorporates green as part of its state colors, although it is primarily yellow and red.

To summarize, the state flag with a green background that stands out is Washington's flag, characterized by its dark green field and the prominent image of George Washington. This flag not only represents the state's identity but also its natural beauty and resources.

For more information on state flags, you can visit resources such as the 50states.com or the National Flag Foundation.