The Greek Cross
also called St. George's Cross and (King) George's Cross
The Greek Cross has all fours members the same shape and form (crux quadrata) and usually represents the Church rather than a symbol of Christ's suffering.
It appears as a 'plus sign' in liturgical documents to indicate where the priest should make the Sign of the Cross. (For example "The peace + of the Lord be + always with + you.")
This cross can be seen on ancient gravestones in the Roman catacombs.
In 958 A.D., a red cross with a white background became the flag of Genoa. In the 12th century, crusaders from England adopted the design for their own use, and took it back to England as the red Cross of St. George. (See Union Flag to understand why this differs from the more familiar "British" flag.)
In Lalibela, Ethiopia, the shape was the template for the monolithic churches (carved from a single block of stone) in the 12th century. Perhaps the most famous is the Church of St. George (Beta Giyorgis), a place of pilgrimage and devotion for Christians, registered by UNESCO as a heritage site, consequently over-visited by tourists, which in turn has led to infestation of corrupt tour guides and other con-merchants. If you go there, caveat lector.
The Greek cross is the basis for the Swastika. Favoured by Adolf Hitler in the Second World War, this variation was a symbol of the extreme-right. The Swastika's history, however, goes much further back.
Another and equally famous variation of the Greek cross is the emblem of the Red Cross. More than one hundred years ago, the International Red Cross was founded to aid those wounded in battle. The objective of the Red Cross emblem was to have a unified distinctive sign that would be respected internationally.
In its most common colour, the Black Cross has been the favourite of several political organisations.
National and regional flags that incorporate the Greek Cross
The Greek Cross doesn't appear on the emblem of the Greek Orthodox Church of Greece (COG); their emblem features the Byzantine double-headed eagle and has a tiny cross atop a crown, (Click image to enlarge), but it does appear on the national flag of Greece.
It also appears on many other national and regional flags, including:
Barceloneta, Puerto Rico
Church in Wales, UK
Democratic Progressive Party of Taiwan
Mantova (Mantua), Italy
Santa Cruz de Mompox, Colombia
Utrecht province, Netherlands
Zhytomyr Oblast, Ukraine
Legend has it that during the Battle of Antioch in 1098, St George rode with the crusaders. In the 14th century St. George became patron saint of the England. (See also Marriott Edgar's monologue George and the Dragon)