
ausgefallen
unusual
Unusual, extravagant, original, or not everyday.
Zu ihrem Geburtstag wünscht sie sich ein wirklich ausgefallenes Geschenk.
For her birthday, she wants a really unusual gift.
unusual / canceled
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unusual
Unusual, extravagant, original, or not everyday.
Zu ihrem Geburtstag wünscht sie sich ein wirklich ausgefallenes Geschenk.
For her birthday, she wants a really unusual gift.

canceled
Canceled; not taking place. Past participle of the verb 'ausfallen' (to be canceled / to fail), used as an adjective.
Wegen Krankheit des Lehrers ist der für heute geplante Unterricht ausgefallen.
Because the teacher is ill, the class planned for today has been canceled.
'Ausgefallen' (unusual / canceled) is the past participle of the separable verb 'ausfallen' (to be canceled / to fail). The two very different meanings of the adjective come directly from the meanings of the verb: something 'fällt aus' (is canceled / does not take place) or 'fällt aus dem Rahmen' (stands out / is unusual).
Morgen fällt die erste Stunde aus.
Tomorrow the first class is canceled.
You can often recognize the meaning from the position in the sentence. If 'ausgefallen' comes before a noun, it means 'unusual'. If it stands alone after the verb, usually 'sein' (to be), it means 'canceled'.
Er hat einen sehr ausgefallenen Modegeschmack.
He has a very unusual fashion sense.
In the meaning 'unusual', 'ausgefallen' often describes things such as: 'ein ausgefallenes Geschenk' (an unusual gift), 'ein ausgefallenes Hobby' (an unusual hobby), 'ausgefallene Kleidung' (unusual clothing), or 'ein ausgefallenes Design' (an unusual design).
Sie sucht ein ausgefallenes Restaurant für ihren Geburtstag.
She is looking for an unusual restaurant for her birthday.
In the meaning 'canceled', the word is used for appointments and events. Typically, 'der Unterricht' (class), 'ein Zug' (a train), 'eine Veranstaltung' (an event), 'ein Flug' (a flight), or 'der Strom' (the power) can be 'ausgefallen' (canceled / out / failed).
Wegen des Sturms ist gestern Abend der Strom ausgefallen.
Because of the storm, the power went out yesterday evening.
down
For a server, down describes its current state: it is not functioning or cannot be reached. ausgefallen more clearly indicates a technical failure as the cause. If only the current state matters, down is appropriate; if the problem itself should be emphasized, ausgefallen is appropriate.

Der Server ist wegen eines technischen Defekts ausgefallen und deshalb nicht erreichbar.
The server has failed because of a technical defect and therefore cannot be reached.
Der Server ist gerade down und deshalb nicht erreichbar.
The server is currently down and therefore cannot be reached.