Gaan (ガーン) is the sound of a sudden shock: bad news hitting you like a gong.
You walk all the way to your favourite ramen shop, and the sign on the door says “Closed today”. For a second you just stand there. That moment is ガーン.
What it means
ガーン is the sound of a big bell or a gong. In manga it became the sound of shock: news so bad that it rings in your head. Today people also say it out loud, half as a joke, when something small goes wrong.
How to use it
Say it on its own, right after the bad news: ガーン! or a slow, sad ガーン…. It usually stands alone; inside a sentence it is rare. To describe the feeling, say ショックです (“I'm shocked”) or がっかりしました (“I was disappointed”).

ケーキは もう ありません。
There's no cake left.

ガーン…。
Nooo...

あした また かいましょう。
Let's buy some again tomorrow.
Close cousins
がっかり is a real everyday word for disappointment, quieter than ガーン. ショック is the English “shock”, used just as in English: ショックです. ズーン is a heavy, gloomy feeling that sinks in after the shock.
In manga and anime
The character freezes, turns white or grey, lightning strikes behind them, and dark lines run down their face. Across it all, in huge letters: ガーン.
Can you use it?
Yes, with friends, for small bad news: no cake, a missed train, rain on your day off. It is playful. For really bad news, say ざんねんです (“what a pity”) or ショックです instead.