Blushing Lines

In manga and anime, diagonal lines drawn across a character's face, over their cheeks, nose, and sometimes ears, symbolize blushing, and are used when the character is embarrassed, flustered, or any other time they're red-faced.

In color, the blushing lines are normally drawn red. In black and which manga, they're black, but even so the black diagonal lines symbolize a reddened face.

Sakura Chiyo 佐倉千代, example of blushing character.

Character: Sakura Chiyo 佐倉千代
Anime: Gekkan Shoujo Nozaki-kun 月刊少女野崎くん (Episode 1)

In text, ///, three or more slashes, can refer to this sort of line to mean blushing.

In Japanese

In Japanese, there are two different terms to refer to this sort of line:

shasen
斜線
Oblique lines. (in general.)
tere-sen
照れ線
Embarrassed lines. Shy lines.

The first term can refer to any diagonal lines, it's not specific to anime, while the second one refers specifically to anime.

Note, however, that since the verb tereru 照れる means "to feel shy," "to feel embarrassed," the second term wouldn't include non-embarrassing cases where a character's face turns red and the lines are used.

Examples

For reference, some examples:

Character: Watanabe Tooru 渡辺通
Anime: Excel♥Saga, エクセル♥サーガ (Episode 4)

Anime: Kuma Miko くまみこ (Episode 1)

hana-di
鼻血
Nosebleed.

Manga: Gabriel DropOut, ガヴリールドロップアウト (Chapter 3)

Context: Satanichia サタニキア shakes with excitement.
zoku'
ゾクッ
*tremble*

Exceptional Examples

The normal blushing line is diagonal and red, and diagonal lines are blushing lines, but there are exceptions.

For example, blushing lines drawn as vertical lines:

Furuhashi Fumino 古橋文乃, Ogata Rizu 緒方理珠, example of parallel vertical lines on background and on a character's face.

Left: Furuhashi Fumino 古橋文乃
Right: Ogata Rizu 緒方理珠
Anime: Bokutachi wa Benkyou ga Dekinai ぼくたちは勉強ができない (Episode 1)

And diagonal lines that aren't blushing lines, but blue lines that symbolize some sort of unwellness.

Gourry Gabriev ガウリイ・ガブリエフ, example of diagonal blue lines.

Character: Gourry Gabriev ガウリイ・ガブリエフ
Anime: Slayers, スレイヤーズ (Episode 2)

Permanent Cheek Lines

Some characters have lines drawn on their cheeks permanently, that stay on regardless of the emotion they may be feeling. Often, these are black lines, but there are cases where the lines are drawn red, too.

The term for these is kote-sen コテ線.