1A casual way to say "sorry" or "my bad" for small mistakes, bumps, or interruptions; more informal than ごめんなさい.
ごめん、待たせちゃった？
Sorry, did I keep you waiting?
あ、ごめん！足踏んじゃった。
Oh, sorry! I stepped on your foot.
ごめん、今日は約束忘れてた。
Sorry, I forgot about our plans today.
ごめんね、うっかりメール送るの忘れてた。
Sorry, I accidentally forgot to send the email.
2A casual call-out used when entering someone's home or room, similar to "excuse me, may I come in?" — a shortened, informal version of ごめんください.
友達の家のドアをノックして「ごめん、いる？」と声をかけた。
I knocked on my friend's door and called out, "Hey, are you home?"
「ごめん、入っていい？」と部屋の外から聞いた。
"Excuse me, may I come in?" I asked from outside the room.
3Permission or leave granted by a superior or authority. An old-fashioned, honorific-style usage rarely heard in everyday modern conversation.
彼は上司の御免を得て、長期休暇を取った。
He obtained his boss's permission and took an extended leave.
江戸時代、町人は役人の御免なしに商売の場所を変えられなかった。
In the Edo period, merchants could not change their place of business without an official's permission.
4Being relieved of a post or dismissed from one's position (御免になる = to be dismissed/discharged). An old-fashioned expression, rarely used in modern Japanese.
不祥事の責任を取り、彼は御役御免となった。
He took responsibility for the scandal and was relieved of his post.
5Used in the pattern 〜はごめんだ to say that one wants no part of something, rejects it, or is fed up with it — "no thanks to X."
残業ばかりの生活はもうごめんだ。
I'm done with a life that's nothing but overtime.
あんな失礼な態度を取られるのはごめんだ。
I won't put up with being treated so rudely.
二度とあの会社で働くのはごめんだ。
No way am I ever working at that company again.