[Most recently updated 7 August 2017]

• Allen and Greenough's New Latin Grammar (at Dickinson College)
• Ancient Greek Tutorialsby Donald J. Mastronarde
• Ancient Greek Tutorials @ AtticGreek.org
• Ancient Sanskrit Online, by Karen Thomson and Jonathan Slocum
• Beginning Biblical Hebrew: A Grammar and Illustrated Reader [Online Companion], by John A. Cook and Robert D. Holmstedt.
• Classical Greek Online, by Winfred P. Lehmann and Jonathan Slocum
• Classical Armenian Online, by Todd B. Krause and Jonathan Slocum
• A Digital Tutorial For Ancient Greek Based on White's First Greek Book Created by Jeff Rydberg-Cox (Classical and Ancient Studies Program, University of Missouri-Kansas City)
• Epigrafía latina: Introducción a la epigrafía latina en ExtremaduraClásica
• Gábor Zólyomi: An Introduction to the Grammar of Sumerian 
• Getting started on Classical Latin
• Greek and Latin Texts with Facing Vocabulary and Commentary: Free digital files for the textbook series written by Geoffrey Steadman 
• Greek Language and Linguistics
• Goodell/ A School Grammar of Attic Greek 
• GREK 1332 online, by Dora Pozzi
• Hack Your Latin, by Michael Fontaine
• Hittite Online, by Winfred P. Lehmann and Jonathan Slocum
• Huehnergard akkadian flashcard sets
• Imperium Latin – free of charge to allBy Stephen Jenkin
• Introducing Ancient Greek (Open University) 
• Introducing Classical Latin
• Introduction to Homeric Greek: Volume 1
• Introduction to Manichaean Sogdian by P. Oktor Skjærvø
• Introduction to Maya Hieroglyphs by Harri Kettunen and Christophe Helmke
• Introduction to Old Avestan by P. Oktor Skjærvø
• Introduction to Old Persian by P. Oktor Skjærvø
• Introduction to Sumerian Grammar by Daniel A. Foxvog / Elementary Sumerian Glossary / Timeline of Mesopotamian History / Chief Figures of the Mesopotamian Pantheon
• Introduction to Young Avestan by P. Oktor Skjærvø
• Introduction to Zoroastrianism by P. Oktor Skjærvø
• Introduction to Manicheism by P. Oktor Skjærvø
• Kurmanji Kurdish: A Reference Grammar with Selected Readings by W. M. Thackston
• LatinPerDiem: Daily Latin lessons in about four minutes, drawn from 2300 years of the corpus
• Latin Teaching Materials at Saint Louis University by Claude Pavur 
• Latinum ElectronicumEd. by Burch, Irene / Hiltscher, Simone / Wachter, Rudolf 
• Learn Ancient Greek, with Prof. Leonard Muellner
• Learning Latin by Luca Graverini
• LIMEN: A Latin Teaching Portal
• Living Latin and Greek
• ምምሃረ፡ልሳነ፡ግዕዝ - MEMHĀRA LESĀNA GE'EZ: RESOURCES FOR LEARNING GE'EZ-- THE CLASSICAL LANGUAGE OF ETHIOPIA 
  
• New Testament Greek Online, by Winfred P. Lehmann and Jonathan Slocum
• New Testament Greek Vocabulary Assessment 
• Old Iranian Online, by Scott L. Harvey and Jonathan Slocum
• The Online Greek Textbook by Shirley J. Rollinson
• Reading Classical Greek (Open Unversity)
• Sorani Kurdish: A Reference Grammar with Selected Readings by W. M. Thackston
• Thus Wrote Onchsheshonqy - An Introductory Grammar of Demotic (Third Edition), by Janet H. Johnson
• Tocharian Online, by Todd B. Krause and Jonathan Slocum
• Tools for Studying the Hebrew Bible
  

Additional resources of thus type are accessible through the  Less Commonly Taught Languages (LCTLs) Project pages at the University of Minnesota.

And see also Lexicity
And see also  Smarthistory, a "multi-media web-book designed as a dynamic enhancement (or even substitute) for the traditional art history textbook"

Textkit has a huge library of Greek and Latin textbooks

Learn Ancient Greek

Listed below is Textkit’s entire collection of Ancient Greek textbooks. All books are made available for full and free download in PDF format.

Greek Answer Keys

A Brief Introduction to New Testament Greek Key, Samuel G. Green

First Greek Book Key, John Williams White

First Greek Writer Key, Arthur Sidgwick

Greek Prose Composition Key, North and Hillard

Greek Prose Composition Key, Arthur Sidgwick

Greek Composition Textbooks

First Greek Writer, Arthur Sidgwick

Greek Prose Composition, North and Hillard

Introduction to Greek Prose Composition, Arthur Sidgwick

Lectures on Greek Prose Composition, Arthur Sidgwick

Selections from the Septuagint, Conybeare and Stock

Greek Lexicon/Dictionary

First Four Books of Xenophon’s Anabasis, William W. Goodwin

Illustrated Dictionary to Xenophon’s Anabasis, John Williams White

Pocket Lexicon of Greek New Testament, Alexander Souter

Greek Reading Text

Book Twelve of The Odyssey in Greek, Richard A. Minckwitz

Easy Selections From Plato, Arthur Sidgwick

Georgics Book IV in Latin, T.E. Page

Plato’s Apology of Socrates and Crito in Greek, Louis Dyer

Prometheus Bound of Aeschylus in Greek, F. D. Allen

Selections From Herodotus in Greek, W. Walter Merry

The Gospel of St. Luke in Greek, H.R. Heatley

The Iliad by Homer Books XIX – XXIV in Greek, Edward B. Clapp

The Odyssey by Homer Books V – VIII in Greek, B. Perrin

Xenophon’s Anabasis in Greek – Book VI, G.M. Edwards

Greek Reference Grammars

Greek Grammar, William W. Goodwin

Greek Grammar, Herbert Weir Smyth

Syntax of the Moods and Tenses of the Greek Verb, William W. Goodwin

Greek Textbooks

A Brief Introduction to New Testament Greek, Samuel G. Green

A First Greek Course, Sir William Smith

A Short Syntax of New Testament Greek, H.P.V. Nunn

First Greek Book, John Williams White

First Greek Grammar Accidence, W. Gunion Rutherford

First Greek Grammar Syntax, W. Gunion Rutherford

Homeric Greek – A Book For Beginners, Clyde Pharr

Introduction to the Language and Verse of Homer, Thomas D. Seymour

NT Greek in a Nutshell, James Strong

Learn Latin

Listed below is Textkit’s entire collection of Latin textbooks. All books are made available for full and free download in PDF format.

Latin Answer Keys

Latin for Beginner’s Key, Benjamin L. D’Ooge

Latin Prose Composition Key, North and Hillard

Latin Composition Textbooks

A New Latin Prose Composition, Charles E. Bennett

Latin Prose Composition, North and Hillard

Latin Reading Text

Caesar’s Civil War in Latin, Charles E. Moberly

Caesar’s Gallic War Commentaries – Literal Translation, Rev. Dr. Giles

Catiline Orations of Cicero – Literal Translation, Rev. Dr. Giles

Cicero Select Orations, Benjamin L. D’Ooge

Extracts From Cicero – Sections I & II in Latin, Henry Walford

Latin Prose Composition Based on Cicero, Henry Carr Pearson

Livy Book XXI in Latin, W.W. Capes

Livy Books I & II in Latin, J.B. Greenough

Ovid’s Metamorphoses – Literal Translation, Rev. Dr. Giles

Select Orations of Cicero – Interlinear, Thomas Clark

Selections From Ovid, Allen & Greenough

The Phormio of Terence in Latin, Fairclough and Richardson

Latin Reference Grammars

A Latin Grammar, Charles E. Bennett

New Latin Grammar, Allen & Greenough

Latin Textbooks

Beginner’s Latin Book, Collar and Daniell

Latin For Beginners, Benjamin L. D’Ooge

Second Year Latin – Part 1 – Selections of Easy Latin, J.B. Greenough

Do you know of others? Do you use any of these in your teaching? Are you developing open access textbooks in any area of ancient world studies? Please respond by clicking the Comments button.