I don't think the question to answer is, "What percentage of your income to save?", but "How much annual income do you need to live?" and "How much do you need to save, and in what ways, to generate that much annual income?"
You must answer the first question I posed, in order to answer the second.
You must also make some assumptions to have any confidence in the answers to either of them. For example, "What annual cost-of-living inflation?" affects the first -- if you can live on $40,000 in 2008, but cost of food, heating, clothing, etc keeps going up 10% a year, you probably can't live on that much in 2018.
You must also make some assumptions about the annual return on your investments, as well as the period you expect to be needing it, to have confidence in the answer to your second question. For example, ideally the amount you have saved will throw off $X (your answer to the first question) for as long as you live. If you can live on $40,000 a year, you'd better be really certain the value of your investments don't go to zero -- either because you're withdrawing too much, or because their value drops -- while you need that income stream.
I can't get perfect answers to some of these questions, so I don't sweat it much; I use rough but plausible numbers. I think of this as navigating a boat (which may make sense only because I've never done that

). I need a compass bearing now, while I'm still a wage-earner. I don't need to know precisely where I'm going, just where I need to go to make landfall. I figure as I get closer to the "shore", I will still have time to trim my course as needed. And, frankly -- and assuming the S doesn't HTF and destroy my ability to save money, and if it does, it kinda moots the whole set of assumptions I've made about how to saving for retirement so that's another issue to tackle separately

-- if I find myself nearing "shore" (desired retirement age) and I'm still not where I need to be, I'll just keep sailing (working) until I reach it. No biggie, assuming I'm not 80 when that happens.
A web site that helped me greatly in this regard is
The Retire Early Home Page, where you will find a lot of discussion over this issue, as well as some calculators that are based on back-tested results. (This is not to say that they are infallible, just that they are based on
something, so that gives me a little more confidence.)
For me, I have reduced that web site's charts to a simple-minded percentage that helps me to answer question #2: I assume that I can withdraw 4% of my investment, "safely". (Meaning, that my withdrawals will never cause the nest egg to hit zero.)
That's a simplification, because that site's charts require to make other assumptions, like, "How many years do you expect to need this income?" and "What mix of stocks/bonds do you expect to have?" But screw it; I use 4% as a "steer-by" number for now. (It's actually more like 3.85% IIRC, but like I said. I'm making the math easier for now.)
So, what if you assume you can live on $40,000 a year? Let's forget cost-of-living inflation for now; "steer-by" numbers, remember. Then this answer to the first question lets you get an estimated answer for the second question: 4% of $1,000,000 throws off $40,000 a year.
If you wanted to live "better", and want $50,000 annually, then that raises your total to $1,250,000.
If you can live on $30,000 annually, that drops your total to $750,000.
After all this, if you can answer those two questions, then the answer to "what percentage to save annually" mostly just falls out of the math. It does depend on other assumptions, like, what rate of return do you expect your investments, while you are making (not withdrawing) them, to give you? And, do you expect your income to be stable or growing? (If not, try to front-load your % as much as possible, because $10,000 invested 20 years from retirement is worth much more than $10,000 invested right before your retirement.) Etc.
Like I said, lots of caveats in there. But I've used them to make what I expect are very conservative predictions of our annual savings rate, and I measure where we are at the end of every year. So far, we're beating the predictions. I'm also not assuming any income from social security, just to be safe. As I get closer to retirement age, I'll figure out what inflation has been doing to my expected annual income needs -- if I can't live on $X any more, then I'll need to keep saving, or figure out how to live on less.
--Steve