X Eyes

In manga and anime, sometimes a character's "eyes turn into X's," me ga batsu ni naru 目がバツになる. Typically, this means they're dead. Well, not dead dead, just dead in the comical sense. Knocked out. Unconscious.

• kizetsu
  気絶
  Faint. (in the sense of becoming unconscious)
  • kasuka
    微か
    Faint. (in the sense of not strong, e.g. a faint light, a faint smell.)
  • kizetsu saseru
    気絶させる
    To make [someone] faint. (causative sentence.)
• shisshin
  失神
  Losing consciousness.

Left: Asuka Ruu 明日香ルゥ
Right: Fudou Devi 歩堂デヴィ
Anime: Kiratto Pri☆chan, キラッとプリ☆チャン (Season 2) (Episode 20)

• Examples
  • Single X Eye

Examples

For reference, some examples:

Character: Illyasviel von Einzbern イリヤスフィール・フォン・アインツベルン
Anime: Fate/stay night (2006) (Episode 20)

Character: Ristarte リスタルテ
Anime: Shinchou Yuusha 慎重勇者 (Episode 1)

• Context: Ristarte falls from a chair.
• Practically identical usage to "spiraling eyes," guruguru-me グルグル目.

Left: Aioi Yuuko 相生祐子
Middle: Naganohara Mio 長野原みお
Right: Minakami Mai 水上麻衣
Anime: Nichijou 日常 (Episode 1)

Single X Eye

Sometimes, the eyes of a character are drawn as one huge X. This is a different thing. In this case, the eyes are supposed to be closed.

Left: Hanabishi Miki 花菱美希
Right: Segawa Izumi 瀬川泉
Anime: Hayate no Gotoku! ハヤテのごとく！ (Episode 10)

That is, this is just >__< with the two eyes merged together. For comparison:

Left: Yoshida Yuuko 吉田優子, Shamiko シャミ子
Middle: Shamisen シャミ先
Right: Hinatsuki Mikan 陽夏木ミカン
Anime: Machikado Mazoku まちカドまぞく (Episode 10)

• Left: ×▽×
• Right: >Д<