There is much discussion about battery-life in use and a standard (CIPA) for measuring it but there is not much information on how long batteries are supposed to last.
How long does a rechargeable Lithium-Ion battery for digital cameras live for?
Is this measured chronologically? (In years, for example) or in cycles? And, if so, what does one know how many cycles a battery has been through?
I've still got several batteries for my 350D, including the one that came with the camera. So that's 10 years, but the capacity isn't what it used to be on any of them. The others weren't original Canon but cheap equivalents, of which two have completely died and at least 2 survived. (I had enough batteries to shoot all day for a week with no reliable power).
Conversely I've seen another Canon battery lose its ability to hold charge in 5 years - it would charge up but be flat again within a day even if not used, and run out quickly in use.
There are a number of different failure modes. In general though, Li-ion batteries lose capacity over time whether used or not, and prefer to be stored with plenty of charge but possibly not full. The effect of cycling on lithium batteries is less than these effects.
Is this measured chronologically? (In years, for example) or in cycles?
Both, I think. At least they're both factors, but I don't think it's possible to reliably predict the useful lifetime. Batteries age whether you use them or just let them sit on the shelf, but they age faster if you put them through a lot of charge/discharge cycles. I'm no expert, but I suspect other factors like temperature and charge during storage have an impact on a lithium ion battery's lifetime.
All these variables probably combine to create a range of possible lifetimes that's probably too large for battery manufacturers to provide a useful estimate. If they guess too low (in either time or cycles), people will accuse them of giving a short lifetime to encourage unnecessarily frequent battery replacement. If they guess too high, people will complain when their batteries don't meet the estimate.
The best thing to do, of course, is to monitor the battery's performance. Does it recharge to the same voltage? Does it provide useful capacity? It can be hard to really know when the performance has dropped if you're not paying close attention. To that end, some cameras (e.g. Canon 6D and recent 5D variants) keep track of each battery's performance so that you can see when a battery might need to be replaced.
Not a very scientific answer, I have had my Nikon D40X battery run for some time now, i think i got this camera when it was launched and still use the stock battery. I have experienced that during cold weather battery drain is faster and in warm it stands up much longer. Also, I believe in deep cycling the batteries. I feel they last a little longer when they are use consistently and allowed to drain almost completely before recharging to full capacity. I have seen some degradation of battery life now after this long which is almost 10 years now.