Do rechargeable lithium-ion batteries exist in standard sizes like AA, AAA, C or D?
Yes, they are finally available. A company called Kentli has released AA and AAA rechargeable lithium polymer batteries that output 1.5 volts.
Update October 2019: I also found Tenavolt batteries which are cheaper than the Kentli, however I have not tested them.
Lithium-ion batteries normally operate 3.7V per cell — but Kentli put circuitry inside the cells to reduce the voltage to 1.5 volts. The company claims that the batteries have a capacity of 2800mWh which matches Eneloop Pro (the NiMH batteries with the highest capacity).
Other Lithium-Ion Rechargeables
A single 18650 battery can replace two CR123A batteries, although at a lower voltage (but much higher amperage). However, the 18650 is a wider cell and will not fit into a flashlight that is designed strictly for the narrower CR123As. Most modern tactical LED lights are designed to use a single 18650 or two CR123As, but it’s best to check before buying. See our article on The Best 18650 Batteries for more information.
There are also numerous other types of lithium-ion batteries made for specific laptops and other electronics gadgets. There is currently no standard size for these lithium-ion cells.