In punctuation, the term ring is usually reserved for the ring above diacritic mark ˚ (looks similar to °). The ring may be combined with some letters of the extended Latin alphabets.
The Danish, Norwegian, Swedish and Walloon character Å (å) is typically seen as an A with a ring above. However, in the languages in which it is used, the letter is seen as a unique symbol, rather than an A with a diacritic.
Other characters with a ring diacritic are Ů and ů (a Latin U with ring above). These characters are used in the Czech language (where the ring is known as a kroužek), together with háček and čárka above many other letters. This vowel "ů" shows how the pronunciation of various words evolved during the centuries. For example, the word "kůň" (a horse; "ň" is softened "n"; pronounce as softened "koon") used to be "koň", which evolved into "kuoň". Ultimately, the vowel "o" disappeared completely, and it is only kept as the ring above "u".
Many more characters can be created in Unicode using the 'combining ring above' U+030A, for example e̊ (e with ring above) or even ń̊ (n with acute and ring above). The ring symbol alone can be created using the character U+02DA.
Half rings also exist as diacritic marks, these are characters U+0351 (combining left half ring above) and U+0357 (combining left half ring below). These characters may be used with the International Phonetic Alphabet. They are here given with the lowercase a: a͑ and a͗. These may or may not display correctly in your user agent.
Other, similar signs are in use in Armenian: the 'left half ring above' U+0559 (ՙ), and the Armenian comma or 'right half ring above' U+055A (՚).
The ring as a diacritic mark should not be confused with the dot above or comma above diacritic marks, or with the degree sign °. Additionally the Angstrom sign Å (looks similar to Å) is seen as a single character, and not as an "A" with ring above.