[Switzerland, i.e.:]
... the plenipotentiaries of 35 nations, assembled in Geneva on July 6, 1906 to revise the Geneva Convention, stated as follows in the enacting clause concerning the symbol of the International Red Cross: "To do homage to Switzerland, the heraldic arms of the Red Cross on a white field, which is formed by reversal of the Swiss Federal arms, shall be maintained as a distinctive emblem of the medical services of most armies." <http://www.eda.admin.ch/washington_emb/e/home/geninf/flag.html>
[And from <http://en.wikipedia.org/wiki/International_Red_Cross_and_Red_Crescent_Movement>:]
The red cross (an inversion of the flag of Switzerland) was adopted as the symbol of the [Red Cross/Red Crescent] movement under the original Geneva Convention. However, in the 1870s, the Ottoman Empire refused to use the red cross and declared that, while it would still recognise the red cross when used by others, it would use the red crescent instead. In 1929, the red crescent, as then in use in Egypt and Turkey, and the red lion and sun, as used in Persia, were both formally recognised as alternative emblems, and this situation is reflected in Article 38 of the First Geneva Convention of August 12, 1949 which recognizes three emblems for the International Red Cross and Red Crescent Movement:
the red cross the red crescent the red lion and sun (not used since 1980, when following the Iranian Revolution, Iran began using the red crescent)
As of 2004, the movement accepts these three symbols and refuses to recognize additional ones, requiring all organisations to accept either the red cross or the red crescent emblems. (These are also the only symbols recognized under the Geneva Conventions of 1949.) Although they are not intended to have any religious significance, they are sometimes seen as religious symbols and thus some nations are not comfortable using them. The religious connotation may also compromise their neutrality in some circumstances.
For this reason, a proposal has been put forth to create a new emblem which would be acceptable to all nations regardless of culture or religion. According to the proposal, individual nations could choose to use the new emblem instead of the cross or the crescent, although the cross and crescent would continue to be permitted and recognized. The new emblem was at one point thought to be the red diamond, which would be neutral yet simple and recognisable (and might perhaps be used in conjunction with an a local symbol, such as the red Star of David used by Israel's Magen David Adom), but little progress has been made to implement this idea. It is not a simple undertaking, since it would require a modification of the Geneva Conventions as well as agreement of all Red Cross and Red Crescent societies.
###
Carl