The following is a list of books that were evidently owned by Joseph Smith.

DeWolf and Brown, First Lines in Arithmetic, for the Use of Young Scholars. Hartford [Connecticut]: Printed and Published by William S. Marsh, 1818.
Location: Wilford C. Wood Collection, Wilford C. Wood Museum, Bountiful Utah

Name in book: Joseph Smiths Book January 31st 1818
Newlots
The name of Catherine, sister of Joseph Smith, is on an inside flyleaf

Mentioned in John Henry Evans, Joseph Smith, An American Prophet (New York: Macmillan, 1933), 437.
Note: According to Evans the First Lines in Arithmetic; also English Reader and Gospel Sonnets (see below) were given by Joseph Smith to a 15 year old boy named Richard Bush in Nauvoo, Illinois. It is not certain if the year that Bush obtained this book was in 1841. His date of birth is given variously as 12 March 1820 and 13 March 1826. Whether 1841 is the correct year of the arrival of Richard Bush is not known.
Pages from these books are reproduced in Wilford C. Wood, Joseph Smith Begins His Work, Vol. 2. Salt Lake City: Deseret News Publishing Co., 1962; middle section.

The Holy Bible, Containing the Old and New Testaments: Together with the Apocrypha: Translated out of the original tongues, and with the former translations diligently compared and revised. With Canne's Marginal Notes and References.
Cooperstown, (N.Y.) Stereotyped, Printed and Published by H. & E. Phinney . . . 1828
[King James Version, with revisions of 1769]
Location: RLDS archives

Flyleaf:
The Book of the Jews And the property of
Joseph Smith Junior and Oliver Cowdery
Bought October the 8th 1829 at Egbert B Grandins
Book Store Palmyra Wayne County New York
Bottom of flyleaf:
Price $3.75
Holiness to the Lord

Joseph Smith's name appears in the Bible.
facing page 24: Joseph Smith Jr. and Oliver Cowd[e]ry Book
Esther: Joseph Smith Jr
page 683: Joseph Smith Jr
facing page 657: Joseph Smith Jr

This Bible was purchased by Oliver Cowdery on 8 October 1829 since Joseph Smith, Jr. was not at Palmyra at the time but arrived at his home in Harmony, Pennsylvania on 4 October 1829. Grandin published the Book of Mormon in 1830. It was used for Joseph Smith's correction of the Bible as markings were made corresponding to his manuscript revisions. Joseph Smith did not know Hebrew or Greek during the time he made the majority of the corrections to the Bible.
At first the full text was written out (for part of Genesis, all of Matthew, Mark and Luke) and then notations. Markings were made in the printed Bible that correspond to the short manuscript notations. Italic words that are crossed out in the Bible represent changes or deletions to be made.
Original manuscripts of Bible corrections in RLDS archives.

"Family Record" under "Marriages" has:
Joseph Smith Junr Emma Hale was married Jan 18 1827 Bainbridge, Chenango County State of New York

"The Phinney's [Henry and Elihu] imported all sorts of books from New York and Philadelphia and distributed them with their own publications through towns and villages from large wagons with moveable tops and counters, even providing a canal boat book store on the Erie Canal" (Margaret T. Hills, ed., The English Bible in America: A Bibliography of Editions of the Bible & the New Testament Published in America 1777 - 1957 [New York: American Bible Society and The New York Public Library, 1961], 69).

Horne, Thomas Hartwell. An Introduction to the Critical Study and Knowledge of the Holy Scriptures, from the 4th corrected edition, illustrated with numerous maps and fac-similes of Biblical Manuscripts. Philadelphia: E. Littell, 1825. 4 vols.
Location: RLDS archives

J D Hughes
Joseph Smith Jun. Kirtland O. Jan - 1834
Note: Vols. 2-4 only contain Joseph Smith's signature
Frederick Madison Smith book plate

Stuart, Moses. A Grammar of the Hebrew Language. 5th edition, corrected and enlarged. Andover, Gould & Newman, publishers and printers, 1835. 271pp.[Fold out materials in back of the book]
Location: RLDS archives

Flyleaf: Joseph Smith Juns Book Bot. Nov. 20th 1835
D. H. Smith
Frederick Madison Smith book plate
Lamoni[,] Iowa[,] Aug. 31, 1895

Note: Joseph Smith along with other church elders took Hebrew lessons from Joshua Seixas in 1836. A certificate attesting to Smith's knowledge of Hebrew was signed by J[oshua]. Seixas on 30 March 1836. (LDS archives)

Augustus Hahn, Biblia Hebraica, Lipsiae, Sumptibus Et Typis Caroli Tauchnitz, 1833. Printed in Hebrew.
Location: RLDS archives

Flyleaf: Joseph Smith jr Book
The signature of D.H. Smith appears in the front cover.
Two scraps of paper were inserted in the book.
Joseph's name is written on the back an inserted sheet titled, "Additional Observations for Discovering the Root": Joseph Smith Jr
Lamoni Church Library Nov 24 - 1922

Smiley, Thomas T. Sacred Geography or a Description of the Places Mentioned in the Old and New Testament, intended to Promote a Knowledge of the Holy Scriptures, accompanied by three maps . . . adapted to the use of schools and Private Families. Philadelphia, Printed for the author by W.P. Bason. Charleston, South Carolina, 1824. 12pp. [Maps: Map of the East as mentioned by Moses; Canaan, Palestine or the Holy Land; Countries mentioned in the New Testament]
Location: RLDS archives

Joseph Smith Jr
M J Whitehead

Robbins, Royal. The World Displayed in its History and Geography, Embracing a History of the World, from the Creation to the Present Day, with General View of the Politics, Religion, Military and Naval Affairs, Arts, Literature, Manners, Customs and Society of Ancient as well as Modern Nations, to which is added, An Outline of Modern Geography. (2 vols. in 1, New York, W.W. Reed, 1832. 408pp.
Location: RLDS archives

name of Z. Coltrin is crossed out
Joseph Smith Jr Book
inside back cover: Cowdery Cowdery

James Gray, Mediatorial Reign of the Son of God (Baltimore, 1821)
Former location: RLDS archives

Mentioned by Fawn M. Brodie, No Man Knows My History: The Life of Joseph Smith (New York: Alfred A. Knopf, 1945), 111. Brodie may have mistaken this book for the one that was owned by Samuel Harrison Smith. See below.

The English Reader [Title page missing] n.d. 224pp.
Location: RLDS archives

Harret Smith
Joseph Smith {Sr./Jr.?]
Harverhill N Y [?]
Samuel

Note: This may not be our Joseph Smith family.

The English Reader
Location: Wilford C. Wood Collection

Mentioned in John Henry Evans, Joseph Smith An American Prophet, 437.

Gospel Sonnets or Spiritual Songs
Location: Wilford C. Wood Collection

Mentioned in John Henry Evans, Joseph Smith An American Prophet, 437.

Samuel Harrison Smith:

Gray, James. The Mediatorial Reign of the Son of God; or, the Absolute Ability and Willingness of Jesus Christ to save all mankind, demonstrated from the Scriptures. In which work an attempt is made to rescue the Gospel call from false philosophy. Baltimore. Published by Cushing & Jewett. 1821.
Location: Harold B. Lee Library, Brigham Young University

on title page: Samuel Smith's Book February 20th 1830

Hyrum Smith

Whiston, William, translated, The Works of Flavius Josephus. Baltimore. Published by Armstrong and Plaskitt. 1830. Purchase date unknown.
Location: LDS archives

inside: Hyrum smiths Book

Alphabetical list of books donated by Joseph Smith to the Nauvoo Library and Literary Institute, 31 January 1844:

Apochryphal Testament
[William] Beaumont[']s Experiments [and Observations on the Gastric Juice]
[James Arlington] Bennett[']s [The American System of Practical] Book Keeping, 2 copies
Book of Mormon
[James] Brown's [An] Appeal, [from the British System of] gram[mar]
[James] Brown[']s [An] English Syntascope
[John Brown] Dictionary of the Holy Bible
Bruns' Travels
Catholic Manual
Catholic Piety
[A.B. Cleveland] Studies in Poetry & Prose
[John F. Dennett] Voyages & Travels of Ross[,] Perry & others
[Orville Dewey] Old World & the New, vol 1st
[Thomas] Dick[']s Philosophy [of a Future State]
[Philip] Doddrige[']s Sermons
[Benjamin Drake] Life of Tecunseh
Epicureo
[Hiram] Gillmore[']s Lectures [on Christianity]
[Charles A. Goodrich] History of the United States
[James] Hervey[']s Meditations [and Contemplations]
Krumanacher[']s Works
Merrills Harmony
Metropolitan[: A Monthly Journal of Literature, Science, and the Fine Arts]
[John Lawrence] Mosheim[']s Church History, 1 Vol
[Joel] Parker[']s Lectures on Universalism
[Parley P. Pratt] Millen[n]ium & other Poems [1840]
Reld & other Travels
[Charles] Rollin, 2 Vol[s]
Sanders Discourse
[Walter] Scott[']s Poetical Works, in 5 vols
Incidents of Travel in Yucatan, by [John L.] Stephens 2 Vo[ls]
[John L.] Stephens Travels in Central America, 2 Vo[ls]
[Henry Philip Tappan] Review of Edward[']s On [the Freedom of] The Will
Times and Seasons 1 2 3 Vol[s] also Vol[s] 1 & 2
[Francois M.A. Voltaire] Historie de Charles [XII]
[Samuel] Whelpley[']s Compend[ium] [2 copies?]
[Samuel Wilcox] Home Physician

List from Kenneth W. Godfrey, "A Note on the Nauvoo Library and Literary Institute," Brigham Young University Studies 14 (Spring 1974):386-89.