It's worth nothing that those generic Chinese phones of various brands actually tend to use one of a very few number of (replaceable) battery variations, which tend to be clones of the battery in common models like the Samsung Galaxy S3. The main variables are width/height/depth/pinout, and the former 3 are usually fixed by the battery manufacturers themselves, while the latter is either from cloning another common product or a reference design.

For bigger lithium-ion cells, 18650 is probably the most common size and has gradually made its way into consumer devices too as a replaceable cell, although the safety implications of the much higher energy density mean they have to be treated more carefully than AA/AAA. (E.g. the warnings about not carrying loose cells because they can short and cause burns or fire is far more important with a lion cell, since they have much higher current capacity.) Companies will continue pushing the "safety" excuse to lock-in users with proprietary batteries, but I see the spread of 18650s as starting to counter that trend.