Batteries and battery chemistries are a huge topic, each worthy of their own page, but I'm going to condense the ones I am interested in here. This page is not exhaustive, it only covers the batteries I've looked into and considered using.

These two families are strongly related, as the electrolytes are both alkali metals. Anode materials often differ.

Lithium Titanate (LTO) uses a crystal structure similar to a perovskite to store energy. It has a huge number of charge cycles, operates well in the cold, can be trickle charged, offers relatively high C ratios (10 is not uncommon), has low ESR and are incredibly safe compared to other lithium-ion technologies. It has lower energy density than other Lithium-ion batteries however, comparable to NiMH.

They don't freeze in temperatures well below 0 which makes them interesting for use in cold environments. This, combined with their safety, makes them extremely interesting for outdoor projects where the extra space and cost is worth it. They're also good for replacing capacitors in some applications, as their self-discharge rate is much slower and they provide a more stable voltage over their operating curve.

Nichicon's SLB are very compact, but the cost per Wh is eye-watering.

Sodium Titanate batteries have been created in research, but I have yet to see any commercially available products yet.

These cells have better cycle endurance than NMC, Li-Po, LiCo or LiMnO4 batteries. They are slightly safer than traditional Li-ion cells, but nowhere near the safety of the LTO cell. They are in between NMC or Li-Po and LTO in terms of energy density.

There are commercially available Na-ion batteries, but their compositions are currently unknown. Supposedly they're safer than lithium-ion batteries, but from what I've seen so far, the only thing that might make them safer is lower energy density. They'll still ignite if you short them out or damage them. Apparently they are also supposed to work better in the cold, but this could be marketing - I haven't seen any evidence for this yet.

NiMH is safer than most Li-ion cheaper than LTO, it's easier for consumers to buy.

These batteries have been made obsolete by NiMH and LTO.

Zinc-air batteries are the most energy dense, COTS primary cell. They require air, can't sustain high current discharge and have a low voltage.

These cells are still widely available for purchase by consumers, and they're cheap. They can technically be recharged, but it's probably not worth it given how cheap nimh and li-ion cells have become.

Might be cheaper than LTO, though if the energy density is substantially worse it would need to be a lot cheaper.

These could be a high density, ecologically friendly alternative to zinc-air batteries.