idioms
I do not listen (but do read) much to English lately, but honestly, I heard it once or twice. Would you consider it old-fashioned?
"I don't mind if I do" said to politely accept an offer of food or drink –
- A: "There's plenty more cake if you'd like another piece."
B: "I don't mind if I do."
Source: Cambridge Advanced Learners Dictionary
Mark my words, the phrase isn't all that outdated.
Nevertheless, I tried to think of other alternatives to this phrase, since that's what you asked for. I manage to think of a few:
Here are some excerpts where these phrases mean roughly the same thing as mark my words:
Don’t say I didn’t tell you: Two years from now, the GOP will officially split into two parties... (from a news article by Charles Ellison, 2014)
And you can bank on this: while crusades may start out as one-man crusades, if the idea behind the enterprise is good, soon you'll have lots of support. (from Magic of Thinking Big, David Schwartz, 1987)
We can teach all the right responses in the world but if we never role model them - well, you can bet your bottom dollar you won't see them in your children. (from a book on parenting by Eydie Comeaux, 2003)
I'm telling you, there's only one way you gonna get to Norlins now, and that's by cab. (from Old Glory: A Voyage Down the Mississippi by Jonathan Raban, 2011)
You can replace the bolded words with mark my words, and the passages will pretty much mean the same thing.
As for the currency of mark my words, an Ngram hints that its usage may have peaked about 100 years ago. Yet even in recent years it still dwarfs some of the alternatives I've mentioned:
I think the most interesting part of that Ngram, though, is the sudden spike in I guarantee it, which seems to coincide with Joe Namath's famous Super Bowl prediction, further discussed in this column.
Off here indicates not the location of living but its source.
The idiom arises in the last half of the 18th century in association with the idiom “get one’s living off (of) the land”, meaning one obtains the income which sustained life by farming or by renting the farmlands one owned to others. Armies were likewise said to “live off the land” or “off the country”—meaning that in wartime they obtained what they needed by appropriating it from the territories they crossed rather than being supplied from home.
A similar use of off appears in the phrase dine off (pheasant, the haunch, six or seven courses) meaning one obtains one’dinner from these sources.
So to say that “She lives off her parents” means she obtains the necessities of life from her parents; to say that “I've been living off rats” means I get my nutrition by eating rats.
Best Answer
It's not that common of an expression, but it doesn't strike me as old-fashioned, either. I disagree a little with the Cambridge Advanced Learners Dictionary here when they emphasize that it's a polite acceptance. It is polite, but more to the point, I'd say it's something like an eager acceptance; it's almost a little playful.