January 20 – Seville in Castile is awarded exclusive right to trade with the New World.
January 24 – Construction of the Henry VII Chapel at Westminster Abbey begins in the perpendicular style, the final stage of English gothic art.
February 11– Queen Elizabeth of York, wife of Henry VII of England, dies on her 37th birthday, more than a week after giving birth to her daughter Katherine Tudor, who died the previous day.
February 13 – Challenge of Barletta: Thirteen Italian knights defeat thirteen French knights near Barletta.
February 23 – French–Spanish Wars in Italy – Battle of Ruvo: The Spanish defeat the French.
April 21 – Battle of Seminara: Spanish forces under Fernando de Andrade de las Mariñas defeats the French under Bernard Stewart, 4th Lord of Aubigny.
April 28 – Battle of Cerignola: Spanish forces under Gonzalo Fernández de Córdoba defeat the French under Louis d'Armagnac, Duke of Nemours, who is killed (considered to be the first battle in history won by gunpowder small arms).
May 10 – Christopher Columbus discovers the Cayman Islands, which he names Las Tortugas after the numerous sea turtles there.
May 13 – Naples is captured by the Spanish.
May 20 (Feast of the Ascension) – Ascension Island is first definitely sighted, by Portuguese admiral Afonso de Albuquerque.
James IV of Scotland and Margaret Tudor are married by Pope Alexander VI according to Papal bull.
The Treaty of Everlasting Peace between Scotland and England is signed; it actually lasts for ten years.
July 23 – Orbital calculations suggest that on this day, Pluto moves outside Neptune's orbit, remaining there for 233 years.
July 30 – Saint Helena is first definitely sighted, by ships of Portuguese navigator Estêvão da Gama returning from the East.
August 8 – King James IV of Scotland marries Margaret Tudor, daughter of King Henry VII of England at Holyrood Abbey, Edinburgh, Scotland.
August 20 – Stephen III of Moldavia concludes a treaty with Sultan Bayezid II preserving Moldavia's self-rule at the cost of an annual tribute to the Ottoman Empire.
September 22 – Pope Pius III (Francesco Todeschini Piccolomini) succeeds Alexander VI as the 215th pope, but dies on October 18.
October 30 – Queen Isabella I of Spain prohibits violence against native tribes.
October 31 – Pope Julius II succeeds Pius III as the 216th pope (some sources list November 1 as the date of election).
December 29 – Battle of Garigliano, near Gaeta, Italy: Spanish forces under Gonzalo Fernández de Córdoba defeat a French–Italian mercenary army under Ludovico II, Marquess of Saluzzo. The French forces withdraw to Gaeta.
Vasco da Gama establishes India's first Portuguese fortress at Cochin.
The Canterbury Cathedral is finished in England after 433 years of construction.
Mariotto Albertinelli paints his work, The Visitation of the Virgin.
Hieronymus Bosch works on the triptych The Garden of Earthly Delights.
Leonardo da Vinci starts work on the Mona Lisa.
The book The Imitation of Christ by Thomas à Kempis is re-published in an English translation.
The pocket handkerchief comes into general use in polite European society.
From this year until 1650, sixteen million kilograms of silver and 185,000 kilograms of gold will enter the port of Seville.
January 3 – Al-Mutahhar, Imam of the Zaidi state of Yemen (d. 1572)
January 11 – Parmigianino (Girolamo Francesco Maria Mazzola), Italian artist (d. 1540)
January 18 – Joachim of Münsterberg-Oels, Duke of Münsterberg, Duke of Oels, Count of Kladsko, Bishop of Brandenburg (d. 1562)
February 2 – Katherine Tudor, English royal (d. 1503)
February 24 – Johann Gropper, Catholic cardinal (d. 1559)
March 4 – Elisabeth of Hesse, Countess Palatine of Zweibrücken, later Countess Palatine of Simmern (d. 1563)
March 10 – Ferdinand I, Holy Roman Emperor (d. 1564)
March 11 – George Harper, English politician (d. 1558)
March 22 – Antonio Francesco Grazzini, Italian writer (d. 1583)
April 6 – Jacob Micyllus, German humanist (d. 1558)
April 18 – Henry II of Navarre, King of Navarre (1517–1555) (d. 1555)
May 1 – Celio Secondo Curione, Italian humanist (d. 1569)
June 1 – Wilhelm von Grumbach, German adventurer (d. 1567)
June 28 – Giovanni della Casa, Italian poet (d. 1556)
June 30 – John Frederick I, Elector of Saxony (d. 1554)
July 23 – Anne of Bohemia and Hungary, Queen consort of the Romans, Bohemia and Hungary (d. 1547)
August 12 – Christian III of Denmark and Norway (d. 1559)
October 4 – Isabella of Portugal, Holy Roman Empress (d. 1539)
November 12 – Philip, Duke of Palatinate-Neuburg, German duke (d. 1548)
November 13 – Ippolita Gonzaga, Italian noblewoman (d. 1571)
November 17 – Agnolo di Cosimo, Italian artist and poet (d. 1572)
November 19 – Pier Luigi Farnese, Duke of Parma (d. 1547)
December 14 or 21 – Michel de Nostredame, called Nostradamus, French physician and writer of Les Propheties (1555) (d. 1566)
December 16 – Lakandula, Lakan of Tondo (d. 1589)
December 20 – Cosimo Bartoli, 16th-century Italian diplomat and writer (d. 1572)
Lucas David, Prussian historian (d. 1583)
Robert Estienne, French printer (d. 1559)
John Frith, English Protestant priest and martyr (d. 1533)
Shimazu Katsuhisa, Japanese nobleman (d. 1573)
Tomé de Sousa, Portuguese nobleman, first general-governor of Brazil (d.1573 or 1579)
probable – Nicholas Bourbon, French poet
February 11 – Elizabeth of York, queen of Henry VII of England (b. 1466)
March 16 – Edward Story, Bishop of Carlisle and Chichester
May 20 – Lorenzo di Pierfrancesco de' Medici, Italian patron of the arts (b. 1463)
June 24 – Reginald Bray, British courtier (b. 1440)
July 3 – Pierre d'Aubusson, Grand Master of the Knights of Rhodes (b. 1423)
August 18 – Pope Alexander VI (b. 1431)
October 10 – Peter II, Duke of Bourbon (b. 1438)
October 18 – Pope Pius III (b. 1439)
November 23 – Margaret of York, wife of Charles I, Duke of Burgundy (b. 1446)
December 14 – Sten Sture the Elder, regent of Sweden 1470–1497 and 1501–1503 (b. 1440)
December 28 – Piero di Lorenzo de' Medici, exiled ruler of Florence (drowned) (b. 1472)
Richard Amerike, English merchant and patron of John Cabot (b. 1445)
Anacaona, Taino queen and poet (b. 1474)
Year 1503 (MDIII) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar.