I recently purchased a reprint of the Nauvoo era periodical, Times & Seasons. As I have read from its pages I have been thrilled with the thought that I am reading the same words the early Saints would have read. In that spirit, I am including a list of early Church periodicals along with dates they were published and links to read either the text or a pdf of the original. Access to each of these is free. Enjoy!
The Evening and the Morning Star (typically shortened to Evening and Morning Star)
Vol. 1: June 1832 - May 1833
Vol. 2: June 1833 - September 1834
To read the original in pdf format click here, to read in html click here.
Messenger and Advocate (click here to read in html)
Vol. 1: October 1834 - September 1835 (click here to read in pdf)
Vol. 2: October 1835 - September 1836 (click here to read in pdf)
Vol. 3: October 1836 - September 1837 (click here to read in pdf)
Elders' Journal (currently I am not able to find any online sources for this periodical)
Vol. 1, No. 1: October 1837
Vol. 1, No. 2: November 1837
Vol. 1, No. 3: July 1838
Vol. 1, No. 4: August 1838
Times and Seasons (click here to read in html)
Vol. 1: November 1839 - October 1840 (click here for the pdf of this volume)
Vol. 2: November 1840 - October 1841 (click here for the pdf of this volume)
Vol. 3: November 1841 - October 1842 (click here for the pdf of this volume)
Vol. 4: November 1842 - October 1843 (click here for the pdf of this volume)
Vol. 5: January 1844 - January 1845 (click here for the pdf of this volume)
Vol. 6: January 1845 - February 1846 (click here for the pdf of this volume)
Millennial Star (click here to read pdf scans)
This was published from 1840 - 1970 and was primarily for the Latter-day Saints in Britain.