The presence of a link should not imply that I agree with or endorse everything therein.

Biblical Hebrew / Aramaic

• The Academy of Ancient Languages
  Includes Hebrew Bible Audio
• Hebrewsyntax.org
  Miscellaneous materials for learning biblical Hebrew
• Ancient Hebrew Grammar
  A plethora of articles on (advanced) biblical Hebrew grammar by Robert Holmstedt and John Cook

Biblical Greek

• Learn to Read New Testament Greek, by David Alan Black
• Dave Black’s New Testament Greek Portal