For small lights and headlamps, I'm still using LSD NiMH AA and AAAs of various flavours. These also live in household clocks, remotes, and computer mice so it's very convenient all around.

Mostly I still use my old Duracell CEF-23 chargers (I have 4). I have a MAHA but only use it when I'm going on a trip, to make sure I don't have a weak battery in the mix.

Years ago I purchased a number of MIC pistol-grip LED spotlights with built-in lithium batteries for $10 apiece. Not expedition quality, but I am surprised and pleased at how well they have held up over time. Some have wall wart chargers. Others have USB chargers built in, and a hatch for the charging cable so it's always at hand.

I occasionally play around with unprotected LiON (18650s?) from discarded laptop batteries. I charge them directly from a 15W solar panel, up to 4.2V (so they don't pop). With a 1A fuse in series, they power any light that's designed for 3 alkaline cells. Crude but effective. I am mindful of the potential fire hazard, but it's nice to have the option.