MightyCall provides such an answer for businesses. With simple, visually-based call flows, adapting your voicemail messages for different customers and even different times of day demands no tech knowledge and no hardware. Try MightyCall’s business phone system free for 7 days, or book a live demo today.
I must be out, or I'd pick up the phone. Where could I be? Believe it or not, I'm not home. The actor, Jason Alexander, recently customized this answering greeting for a big fan, Kat Dennings. Watch the full segment on Youtube here.

5. "Hello, [Person's name] is chasing new adventures and is no longer with [Company name]. Please forward all future requests to [New or interim person's name] at [phone number]. Thank you!"
nothing too crazy in terms of actual content, but my brother and i recorded our message in irish accents a while back, which was quite fun. we fooled plenty of people (i'm sure had any true irish folk called, they'd have vomited at the poor accent impersonations!) Aug 1, 2004 19,801 8 The City of Culture, Englandshire I did one once where I just said "hello?" - then paused for a few seconds and continued ... Quite a few people said they started talking before being interrupted by me telling them to leave a message! I've heard messages like that before – although they've kept on saying "hello?" a few times (louder and louder) to make you think that they've actually answered the phone but they can't hear you.