Since the early 80s, I have used rechargeables for my flash equipment that I used in photographing weddings. I started off using the "nickel-cadmium (Ni-Cad) for about 15 years and, as those wore out and wouldn't hold a charge, switched to the "nickel-metal hydride" (Ni-MH) batteries. I have yet to see any rechargeable "lithium-ion" (Li-on) batteries in the normal sizes (AA, C, & D).
While Li-on batteries have very little "memory problems" like the old NiCads did, ALL rechargeables only put out 1.2 volts. Many electronics do not work well at less than 1.5 volts which is what you get in regular batteries. Also, there is not a rechargeable battery made that can last as long primary single use batteries. AND, while the primary batteries get weaker slowly, giving you time to find replacements, all rechargeables go dead as if they fell off a cliff.
Some have suggested using lights that can use either rechargeables OR a primary use batteries and this is an excellent question. But how easy is it to find that battery used in so many lights these days, a CR123 (or whatever the number is) when you are out camping? You're better off using the AAA - D types of batteries as those can be found virtually everywhere.