Terminology:
"Wide" characters take two cells. "Narrow" characters take a single cell. "Ambiguous" characters resolve as either "Wide" or "Narrow" depending on the terminal emulator's configuration.

At the time of writing Unicode 13 is the current version. No claims are made about unreleased Unicode versions.

The following character is always Wide:
|ｅ|
0123

The `ANGRY FACE (U+1F620)` below is Narrow in Unicode 8 and Wide in Unicode 9 and up:
|😠|
0123

The `GREEK CAPITAL LETTER ALPHA' (U+0391)` below is ambiguous width in Unicode 8 and up:
|Α|
0123

The `UMBRELLA WITH RAIN DROPS (U+2614)` below is ambiguous width in Unicode 8 and Wide in Unicode 9 and up:
|☔️|
0123

The `SQUARED THREE D (U+1F19B)` below is supported in Unicode 9 and later and is ambiguous width.
|🆛|
0123