The answer? As many or as few as makes you comfortable and happy without you know, bankrupting you. But the "tradition" of even measuring a ring's worth by salary was all the start of a De Beers advertising campaign and was designed to push up profits.
This BBC article on the subject notes: "In the 1930s, at the start of the De Beers campaign, a single month's salary was the suggested ring spend. In the 1980s in the US, it became two months." I don't know when the "standard" bumped up to three months, but that's the number I've always heard thrown around in casual conversation the one or two times it's come up.
This suggestion changes based on the culture, apparently, as well.
"In the UK, writes Rebecca Ross Russell in Gender and Jewellery: A Feminist Analysis, the advertisements kept the single month's pay suggestion. But Japanese men were urged to spend three months' salary. 'The salary rules were a stroke of genius,' writes Russell, who believes De Beers managed to entwine western values with the Japanese sense of honour. 'A diamond engagement ring: worth three months' salary,' ran one of the adverts in the 1970s. Japan remains one of the leading markets for diamond jewellery."
These advertising campaigns do seem to work; On the eve of World War Two, only about 10% of engagement rings contained diamonds. That number jumped to 80% by the end of the 20th century.
The website Credit Donkey stated this year that Americans spend an average of about $5,500 (U.S) per engagement ring, with people in the UK spending about $2,000, and Australians about $5,000. I really do have to question who they're surveying though; I don't exactly go about asking people how much their rings cost (and in fact, would rather not know for the most part), but that seems on the high end to me, and as can be seen on the annual Knot wedding statistics report, there is a bit of a self selecting bias toward people willing to spend more money on these things.
As Credit Donkey points out, this "standard" doesn't particularly make sense these days, as most people get married in their late 20s when they haven't yet reached their full earning potential, and most also graduate with student debt. Thus, spending thousands of dollars on a ring may actually not be feasible for your average person wanting to get married.
As for myself - my Victorian-era engagement ring actually came from a vintage jewelry store in the Chicago suburbs where John and I used to live (I moved to DC for work, not certain when we'll be living together again, alas.). I actually picked it out myself back in September (yeah that lovely proposal at the Eiffel Tower Restaurant in November on our four year anniversary trip to Las Vegas wasn't actually that much of a surprise, lol). It's a gorgeous gold double trefoil gem set ring and I've never seen anything else like it; I love it in every way. But I can tell you that it definitively did not cost three months of John's salary (he approved of me writing about this beforehand and apparently I'm not allowed to go into any more detail on that, hah). I think I'd be really uncomfortable to wear something that valuable on my hand day after day, really; I'm a bit too klutzy to feel safe doing that. Fortunately, my ring itself is so unusual that no one has ever given me or John any crap over it. Yay!