AA batteries for almost everything I use every day - flashlights in particular, the Red Rock lantern etc. But an important exception for my headlamps, which aside from the Fenix 1xAA light in my pocket, are my go to source of light in an emergency.

I buy a bulk 32xAA standard alkaline package at least once a year - I feed these to my son, who seems not able to differentiate between rechargeable and non-rechargeable batteries and has fried at least one charger because of it. He uses them in his toys most of the time. I also like to have a certain number of alkaline batteries around just in case - if the lights blow, and are going to stay off for a while, a pocketful of alkalines are comforting. And I'm way more likely to hand a friend (let alone a complete stranger) 4xAAs alkaline rather than 4xAA eneloop or NIMHs. When our power was out for 9 days a couple years ago, I had to make specific allowance for recharging my NiMHs, kind of a hassle.

AA eneloop and NIMHs - I really like eneloop, they don't trickle out charge nearly as much as NIMHs. I don't think we can have enough of these, I buy them when I find them on sale. NIMHs mostly in everday devices, like TV remotes, also in my camera, fenix and minimaglites in glove compartments, first aid kits etc etc Sony via Costco in their eneloop SKU distributes neat C and D sized shells that you can slip a single AA battery into, I'd like to use those on my World radio that takes 8xC type batteries.

AA lithiums, about 12 or so, socked away in my earthquake supplies. Good for a long time, when I need them they should be there.

AAAs, only for a TV remote and a Petzl headlamp I still use sometimes hiking. If I ran out of AAAs though, I'd be okay with another headlamp, which is

The Doug Ritter headlamp, runs on 2xCR2032s. I own several of these ($15.95 per, why not) Usually a pricey battery, but I bought a bunch online for very cheap, their charge doesn't trickle away either. Keep one in my first aid kits (4 total), one in my backpack, another in my daypack. Good, reliable strong beam of light, no hands, inexpensive. I love the small size of the CR2032 battery, easy to pop in spares wherever the headlamps live.

Also I found 6xCR123 in my sock drawer the other day, and had to think what they were for. For my green Glo-Toob, I'd forgotten them but I bought them with the CR2032s for cheap online and use them to replace the default. But after 20-30 hrs of glowing, no replacement necessary so far, and I doubt I would remember to pack them along with the GloToob itself. Its a neat source of light or glow, but not critical for me most of the time.