Minecraft saves the world data and the player data. Saving the world data is done in multiplayer and singleplayer with the same method. It saves everything in a single
Previous versions of minecraft saved the data in a file structure with many files, which was slower, I think.
I don´t know this exactly, but I guess that a database for world saving would be not the best, because the data is saved in intervals of 15 minutes or so and a database is not designed for saving all data at the same time.
The player data on multiplayer servers is saved in a
.dat file. I don´t think that this player data is saved in a SQLite database or something similar, because using a database for requesting once and saving every 5 minutes or so is also not the best.
To sum it up:
I think Notch doesn´t even use any database, because it does not make sense since every data is kept in memory and only saved in intervals of minutes.