SQLite is likely used more than all other database engines combined. Billions and billions of copies of SQLite exist in the wild. SQLite is found in:
Since SQLite is used extensively in every smartphone, and there are roughly 3.5 billion (3.5e9) smartphones in active use, each holding hundreds of SQLite database files, it is seems likely that there are over one trillion (1e12) SQLite databases in active use.
SQLite is probably one of the top five most deployed software modules of any description. Other libraries with similar reach include:
Libc is omitted from the above list even though it is more common than SQLite because libc is not a single software component but rather several competing implementations (ex: BSD vs. GNU) with similar interfaces. There are also independent implementations of libjpeg and libpng, though in those cases the canonical implementations are very popular.
Precise numbers are difficult to obtain and so exact rankings are impossible. But our best guess is that SQLite is the second mostly widely deployed software library, after libz. Some commentators observe that SQLite tends to be statically linked and thus have multiple instances on each machine, whereas libz tends to have just a single instance per machine in the form of a shared library or DLL. So even though the number of devices containing libz may be greater than the number of devices that contain SQLite, the total number of instances per device might be higher for SQLite and so SQLite might be the single most widely deployed and used software component.