There's several different databases. A lot depends on the time period and language(s) you're looking for.

The primary resources for Early/Middle Bronze Age texts are CDLI (wide variety of cuneiform texts), ETCSL (Sumerian literature), ARCHIBAB (Old Babylonian), and CTH (Hittite). There is also the new Leiden Electronic Corpus of Hittite Texts, but it requires registration, and I haven't yet used it.

For the Iron Age, the State Archives of Assyria are extremely useful.

ORACC has several projects in addition to the SAA that may be of interest.