Access Text Study Resources Online

Torah

Scroll down to the heading This Week's Torah Portion and look below the heading.
For an overview, select the name of the parashat.
For commentary, select View [parashat name] Commentary.
For the text, select Read Full Text of text of [parashat name] (CCAR translation from The Torah: A Modern Commentary).

Visit Sefaria's Torah Portions page and select the correct parashat.
For the text, read the parashat directly from that page or select Read the Portion (JPS translation from Tanakh: The Holy Scriptures).
For commentaries, select Sheets and choose a commentary.

For an overview, look to the right-hand menu and select Text & Summaries, then [parashat name] in a Nutshell.
For the text, look to the right-hand menu and select Text & Summaries, then [parashat name] Torah Reading (Rabbi A.J. Rosenberg's translation; you can use the button at the top of the translation to turn on Rashi’s commentary).

Read introductions to Talmud on My Jewish Learning (short) and Chabad (long). View a guide to the layout of the Babylonian Talmud.

Babylonian Talmud, a.k.a. Talmud Bavli (more detailed, and considered more authoritative than the Jerusalem Talmud) resources:

Michael J. Rodkinson's 1918 translation (pdf) and HTML (webpage) versions of many tractates on the Jewish Virtual Library
Soncino Babylonian Talmud, Ed. I Epstein, 1935-1952, on Halakhah.com
The William Davidson Talmud on Sefaria (read about the WD Talmud)
Chabad's Study Talmud page - numerous resources.
RealClearDaf presents both sides of a Bavli Talmud page and has an audio lesson to accompany; register for free to access other days.
HebrewBooks' scanned and OCRed version (under "Shas," another term for Talmud)
BavliOnline's manuscripts (they load slowly)

Heidi Lerner lists other online resources in an article for the Association for Jewish Studies.