Conference.lds.org has conference talks in English back to 1971. PDFs are available for conferences since 2008 and EPUB files since 2011. Many other languages also appear in these formats but not all the way back to 1971.
The Church History Department has scanned all the General Conference Reports in English since 1880 and placed them online in the Internet Archive, a non-profit Internet library.
BYU’s LDS Scripture Citation Index (scriptures.byu.edu) has the text from conferences from 1942 to the present. You can search them or check references in all conferences to a given scripture passage.
Conference Video and Audio
Conference.lds.org has video and audio in English from 1971 to the current conference. Video back to 2008 is also available in more than 70 languages. Some missing sessions will be filled in over the next few months.
Go to a specific conference at conference.lds.org and then click “Show Music” at the top of the page to see the music performed at the conference by the Mormon Tabernacle Choir and other choirs. You can then choose to watch, listen, or download the music.
You can also see an index of all the music by clicking “All Music” in the left-hand navigation at conference.lds.org (or go there directly at GCmusic.lds.org). In the index, you can search across multiple archives and conferences. Listen to the music by clicking the Play button at the beginning of any row or download the music by clicking the download link at the end of the row.
The archive goes back about 18 years, and more music is being added all the time.