Cursive-based letters

A few letters have the forms of cursive or script letters. Examples:

Note

Ligatures

Ligatures are called precisely that, although Unicode often mistakenly calls them "digraphs" and some have dedicated names, such as ash and ethel. Examples:

Rotated letters

Many letters are turned, or rotated 180 degrees. Examples:

Notes

A few letters are reversed (flipped on a vertical axis):

Notes

One letter is inverted (flipped on a horizontal axis): ʁ inverted capital small R. (ʍ could also be called an inverted w, but turned w is more common.)

Letters with extra lines, curls and serifs

When a horizontal stroke is added, it is called a crossbar: ħ barred h, ɵ barred o, ʢ reversed barred glottal stop or barred ayin, ɟ barred dotless j or barred gelded j (apparently never 'turned f'), ǂ double-barred pipe, etc.

One letter instead has a slash through it: ø slashed o.

The implosives have hook tops: ɓ hook-top b, as does ɦ hook-top h.

Such an extension at the bottom of a letter is called a tail. It may be specified as left or right depending on which direction it turns: ɳ right-tail n, ɻ right-tail turned r, ɲ left-tail n, ʐ tail z (or just retroflex z), etc. But note: ŋ eng or engma, ɱ meng, ꜧ heng.

When the tail loops over itself, it's called curly: ʝ curly-tail j, ɕ curly-tail c.

There are also a few unique modifications: ɬ belted l, ɞ closed reversed epsilon (there was once also a ɷ closed omega), ɰ right-leg turned m, ɺ turned long-leg r (there was once also a long-leg r), ǁ double pipe, and the obsolete ʗ stretched c.

Several non-English letters have traditional names: ç c cedilla, ð eth (also spelled edh), ŋ engma or eng, ə schwa (also spelled shwa), ǃ exclamation mark, ǀ pipe.

Other symbols are unique to the IPA, and have developed their own quirky names: ɾ fish-hook r, ɤ ram's horns, ʘ bull's eye, ʃ esh (apparently never 'stretched s'), ʒ ezh (sometimes confused with yogh), ɧ hook-top heng.

The ʔ is usually called by the sound it represents, glottal stop. This is not normally a problem, because this symbol is seldom used to represent anything else. However, to specify the symbol itself, it is sometimes called a gelded question mark. This latter name is derived from its original form as a dotless question mark in a fashion reminiscent of gelding.

Traditionally named diacritics

é acute, ē macron, è grave, ê circumflex, ě wedge or háček, ë diaeresis or umlaut, ĕ breve, ẽ (superscript) tilde, plus variants such as ḛ subscript tilde, ɫ superimposed tilde, etc.

Non-traditionally named diacritics

d̼ seagull, e˞ hook, e̽ over-cross, d ̚ corner, d̪ bridge, d̺ inverted bridge, d̻ square, e̥ under-ring, e̊ over-ring, e̜ left half-ring, e̹ right half-ring, e̟ plus, e̠ under-bar, e̯ arch, d̬ subscript wedge, e̝ up tack, e̞ down tack, e̘ left tack, e̙ right tack, d͡z tie bar, ẹ under-dot, n̩ under-stroke.

Diacritics are alternately named after their function: The bridge is also called the dental sign, the under-stroke the syllabicity sign, etc.