Inscriptions
EDCS - Epigraphik-Datenbank Clauss-Slaby. Extremely large database that records almost all Latin inscriptions. If you cannot find it here, it may not exist. Started and maintained Manfred Clauss
EDH - Epigraphische Datenbank Heidelberg. Large database including an Epigraphic Text Database, an Epigraphic Bibliography and a Photographic Database. Particularly good at inscriptions outside the main editions.
Papyri
Papyri.info. A website dedicated to the study of ancient papyrological documents. It offers links to papyrological resources, a customized search engine, and an editing application, the Papyrological Editor, which contributors can use to suggest emendations to texts. It includes the Duke Databank of Documentary Papyri.
APIS (Advanced Papyrological Information System). APIS is a collections-based repository hosting information about and images of papyrological materials (e.g. papyri, ostraca, wood tablets, etc) located in collections around the world.