The very first such database was the Bar Ilan Responsa Project, which began in 1963 at the Weizmann Institute in Israel, migrated to Bar-Ilan University soon thereafter, and was up and running by 1967.
It became available in time-sharing mode from university terminals in 1979, was transferred to CD-ROM in 1990 and in the mid 2000s to flash drive, and version 1.0 was offered for sale to the public in 1992.
It also features approximately 360,000 hypertext links between the various collections within the database, as well as a topical halakhic index for the Shulchan Aruch and selected responsa.
Since its early years it has employed a sophisticated search-engine specifically designed for Hebrew language texts.
It has less in the overall area of Halakha and fewer responsa, but rivals Bar Ilan's Reponsa project in: Jewish philosophy and Mussar.
In recent years, Bar Ilan has included a great number of texts that considered to be mostly accurate, and mostly error free and has become the gold standard of any Torah database.
Criticisms: It does not have extensive hypertext links between its various large collections, the texts are considered to be inaccurate and may have some errors in them.
Otzar ha-Poskim (also see below) produces "The Torah Bookshelf," a large digital collection of basic texts called "Halamish" (Ha-Sifriyah ha-Toranit) in Hebrew, currently in version 3.0.
Tanakh with both vowels and cantillation signs is available in the Mikra'ot Gedolot Haketer package and as online freeware from Mechon Mamre, Hebrew Wikisource and Base HaSefer (see the latter three below).
The Mishnah is included as a keyed-in digital Hebrew text with vowels in all of the general software packages above.
Text study projects at Wikisource allow contributors to help build free content Torah databases at Wikimedia through volunteer typing and editing.