The register matters more than the word. माफ़ कीजिए literally means "forgive me" and is genuinely apologetic — you would use it for stepping on someone's foot, for being late, for a mistake that cost somebody something. Using it for brushing past a person in a queue sounds theatrical.
For minor things, सॉरी is what people actually say, in English, in the middle of a Hindi sentence. This is not a failure of the language — it is how urban Indian speech works, and reaching for a Sanskritic alternative to avoid it makes you sound like a newsreader.
English "excuse me" splits into two in Hindi. To get past someone or to interrupt, सुनिए (suniye) — literally "listen" — which is polite despite how it translates. To apologise, माफ़ कीजिए.
मुझे बहुत अफ़सोस है (mujhe bahut afsos hai) — I am very sorry, in the sense of regret rather than apology. This is the one for condolences and for serious mistakes, and it is noticeably heavier than माफ़ कीजिए.
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