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After watching some tear-down videos on YouTube with various lithium battery products (portable chargers, laptop battery, power tools) they all (apart from mobile phones / tablet battery) seem to feature cylindrical battery cells.
Is there a technical reason for this, other than it's a uniform size that tiles relatively well to give manufacturers flexibility in incorporating the cells?
1) The cylindrical shape is very easy to manufacture - You basically fold the layers around a round object.
2) For the same reason as drinks cans - this shape is something between the Sphere (high strength and damage resistant) and Cuboid (Easy to stack and low space is wasted). It is the best trade-off between strength and volume.
3) This way You can easily stack the batteries - (Parallel and Series connections).
Among other reasons already stated, in 1991 Sony commercialized the first lithium-ion cell and later used it to power their 8mm camcorder. They needed a way to make these new batteries quickly and on a huge scale. At the same time CDs were killing tape sales (remember cassette tapes?). The same equipment that coated magnetic tape with slurry could be used to make batteries in the same way. So basically they had a bunch of equipment and factories that were slowing down and it all kind of lined up. That's why it started that way anyway.
That's a pretty well told story in the industry and if you google you'll probably find a few articles about it. Everyone peddling some new version of the Lion battery or some new battery technology likes to lead with it to show you how old and outdated the batteries you're currently using are.
I'd say the opposite is the case.
Nearly all alkaline cells (and zinc carbon etc.) are round. The square-ish packs are made up of round cells (e.g. 9V; the larger sizes such as lantern batteries often use C or D cells internally).
The main exceptions are lead-acid and lithium, such as phone batteries. Many small rechargable devices like MP3 players and even my current laptop use these "prismatic" or "pouch" cells as well, which minimise the packaging bulk and weight.
Note that some round Li cell sizes are the same as the common alkalines (14500 is the same as AA but ~3x the voltage which leads to useful tricks to free up space)
A cylinder (or even better, a sphere, but a spherical battery isn't a very convenient shape to use inside a device) is a much more efficient use of material for resisting internal pressure than a box with flat sides, in case the battery fails or overheats.
With a box shape, the sides can bulge outwards and then break off where they join at the edges. A cylinder doesn't have any "edges" except where the end pieces join the cylindrical wall.
Aside from the stress analysis considerations, the shape with the biggest ratio of enclosed area to circumference is also a circle - so even for an unpressurized container, a cylinder uses the least material to hold a given volume. For the same volums, a square section container has about 27% more surface area than a cylindrical one - and that means 27% less "dead weight" and material cost.
The simplest reason there are a lot of round cells is the reason that tek states in his comment. The batteries consist of two electrodes seperated by an electrolyte, one set gives the normal voltage. To increase capacity and current capability, the electrodes and seperator are typically very thin and are wound up into a "jelly roll". The easiest way to do this is simply wind it up into a coil and seal it in a can. Hence the round cells.
Prismatic cells, the rectangular ones used in phones and similar electronics, are made in a similar way, they are simply flatter and oblong. This is why a lot of prismatics will have a curved edge.
