The Thesaurus Linguae Graecae is a digitized collection of literary texts written in Greek from Homer to the fall of Byzantium in AD 1453. The site also includes several digitized lexica. To use the site, first register for an account (see the link in the top-right of the TLG site).
Thesaurus linguae Latinae (TLL)
Developed at the Bavarian Academy of Sciences, the Thesaurus linguae Latinae (TLL) is a dictionary of ancient Latin based on literary and non-literary texts from antiquity up to 600 AD.
Note: The open access version is essentially a collection of very large pdf files. For best results and easier navigation, download the section you wish to look at to your own computer, then open the pdf to view the bookmarks.
Logeion, from the University of Chicago, is a set of lexica for Latin and ancient Greek.
The Searchable Greek Inscriptions database presents inscriptions from multiple references. Browse by region, reference source or search.
The site Classical Latin Texts from the Packard Humanities Institute presents Latin literature in full text, and also allows for keyword searching. The site also has a concordance.
Papyri.info allows you to search through and browse ancient papyrological materials and includes images. The site is curated by scholars and includes translations and commentary from scholars.