Links to photos of extant 15th-17th century carpets, as well as depictions of carpets in 15th and 16th century artwork.
See also Turkish Rugs In European Paintings and more links on pre-17th century rugs and carpets .
If you are interested in embroidering a carpet, read Portuguese Needlework Rugs, also called Arraiolos Carpets ; a discussion of the manufacture of a carpet embroidered for the Australian SCA can be found at The Royal Carpet .
Carpets used as bench-coverings in Guiron le Courtois (BNF NAF 5243), c. 1370-1380:
Arthur and Bedevere play chess (fol. 3v),
Arthur and the messenger of Gaunnes (fol. 6),
Brunor of Estrangor and Lac of the Black Isles (fol. 70), and
Meliadus and his host (fol. 73v)
Detail from The Arnolfini Marriage by Jan van Eyck, 1434
Suckling Madonna Enthroned by Jan van Eyck, c. 1436
Small Triptych by Jan van Eyck, c. 1437
The dubbing of William II of Holland , Chronografia (BNF Fr. 9002, fol. 94), mid-15th century
An interesting heraldic carpet in the presentation scene , History of Alexander (BNF Fr. 9342, fol. 5), mid-15th century
Madonna and Child with Saints by Alessio Baldovinetti, 1454
The Continence of Scipio from the workshop of Apollonio di Giovanni, c. 1463 (V&A 5804-1859)
Detail from the handwashing of Pilate from the Schottenaltar, c. 1469-1480
The Court of Mantua by Andrea Mantegna, 1471-74
Montefeltro Altarpiece by Piero della Francesca, 1472-1474
The Donne Triptych (center panel ) by Hans Memling, c. 1475
St. Sebastian by Antonello da Messina, 1476-77
Detail from Madonna and Child Enthroned with Saints by Domenico Ghirlandaio, c. 1479
Madonna and Child with Angels by Hans Memling, after 1479
St. Jerome in his Study by Domenico Ghirlandaio, 1480 (this webpage notes that it seems to be the same carpet as his Madonna and Child Enthroned below)
Virgin Enthroned with Child and Angel by Hans Memling, 1480
Confirmation of the Rule of the Order of St. Francis by Domenico Ghirlandaio, 1482-85
Madonna and Child Enthroned with Saints by Domenico Ghirlandaio, 1483 (see also Domenico Ghirlandaio and his Rugs )
Portrait of a Young Man by Hans Memling, 1485-90
Virgin and Child Enthroned with Two Angels by Hans Memling, 1485-90
Annunciation with St. Emidius by Carlo Crivelli, 1486
Flower Still-Life by Hans Memling, 1490
A diptych with two members of the shoemakers' guild as donors , Aert van den Bossche, c. 1491-1500
Meeting of the Betrothed Couple and the Departure of the Pilgrims by Vittore Carpaccio, 1495 (with good details here and here )
Manuscript miniature of King David, workshop of Girolamo dai Libri, c. 1495 (V&A E.1168-1921)
The Mass of St. Gilles , 1500
Birth of the Virgin by Vittore Carpaccio, 1504-1508
Madonna and Child with Sts Peter, Christine, Liberale, and Jerome by Lorenzo Lotto, 1505
The Baptism of the Selenites by Vittore Carpaccio, 1507
Cardinal Bandinello Sauli, His Secretary, and Two Geographers by Sebastiano del Piombo, 1516
Portrait of a man by Moretto da Brescia, c. 1520-1525
A Family Group by Bernardino Licinio, 1524
Portrait of Laura Pisani , circle of Dosso Dossi, 1525
Virgin and Child by Jan Provost
Madonna and Child with Saints by Lorenzo Lotto, 1521
Husband and Wife by Lorenzo Lotto, 1523
Darmstadt Madonna by Hans Holbein the Younger, late 1520's (detail , commentary )
Portrait of the Merchant Georg Gisze by Hans Holbein the Younger, 1532 (detail
Jean de Dinteville and Georges de Selve (The Ambassadors) by Hans Holbein the Younger, 1533 (detail 1 and detail 2 )
Supper at Emmaus by Jacopo Bassano, 1538
Portrait of a Lady in White by Moretto da Brescia (detail ), c. 1540
Dives and Lazarus by Bonifacio Veronese, 1540s
The Alms of St. Anthony by Lorenzo Lotto, 1542 (also here )
Portrait of an unknown couple by Lorenzo Lotto, c. 1543
Portrait of Archbishop Cranmer by Gerlach Flicke, 1545-46
Giovanni della Volta with his Wife and Children by Lorenzo Lotto, 1547 (also here )
Portrait of a young woman , c. 1550
The Welbeck (Wanstead) Portrait (Queen Elizabeth I) by Marcus Gheeraerts the Elder, c. 1585
Portrait of Queen Elizabeth I , c. 1592
The Last Supper by Otto van Veen, 1592
The Lute Player by Caravaggio, 1600
Supper at Emmaus by Caravaggio, 1601-1602
Portrait of an unknown lady , c. 1603
The Somerset House Conference , 1604
Portrait of Princess Elizabeth by Robert Peake the Elder, c. 1606
Supper at Emmaus by Caravaggio, 1606
Portrait of Lady Diana Cecil by William Larkin, c. 1614-18
Early Examples of Offset Knotting includes photos and descriptions of several rugs from the 13th-16th centuries. Elsewhere on the same website are instructions for a simple frame loom for making carpets.
Some more extant carpets:
Detail of knotted pile wool rug , Turkey, early 14th century
Detail of knotted pile wool rug , Turkey, early 14th century
Detail of knotted pile wool rug , Turkey, early 14th century
Admiral Heraldic Carpet with the heraldry of Fadrique Enriquez de Mendoza (1390-1473)
Carpet , first half of 15th century, Spain
Small-pattern Holbein carpet , Spanish (Mudejar), Spain, (Probably Alcaraz), 15th century
Armorial carpet made in Islamic Spain, 15th century
"Holbein" carpet , Ottoman Turkey, 15th century
Silk-velvet carpet , Turkey, 15th century
Holbein Carpet , late 15th century
Silk carpet with gold threads , Ottoman, 15th-16th century
Prayer rug , Ushak region, Turkey; late 15th-16th century
A 'Small Pattern Holbein' rug , first half of the 16th century
The Ardabil carpet , Iran, 1539-40
The Ardabil carpet, Iran, 1539-40 (V&A 272-1893)
Carpets from 16th century Iran (V&A 326-1894; 23-1883; 670-1896; T.267-1959; 579-1884)
Carpet with animal decorations and central medallion , Iran, 16th century
'Small-pattern Holbein' carpet , Anatolia, 16th century
Holbein carpet with small motifs , Anatolia (Ushak region), 16th century
Holbein carpet with large motifs , Turkey, 16th century
Prayer-carpet , Turkey, 16th century
Knotted pile wool rug fragment , Turkey, 16th century
Knotted pile wool rug fragment , Turkey, 16th century
Small-pattern Holbein carpet, Turkey, 16th century (with abstract for an article, "Knots of Desire: An investigation into the importing of Oriental Carpets into England 1581-1640")
"Lotto" rug , Ushak region, Turkey, 16th century
Fragment of a large pattern Holbein carpet , Anatolia, 16th century
Table carpet made in Egypt or Turkey in the mid-16th century (V&A 151-1883)
Carpet, Turkey, 1550-1600 (V&A 903-1897)
The Mantes carpet (corner detail ), northwestern Iran, late 16th century
Kilim carpet with scenes from legends , late 16th-early 17th century
Carpet, Iran, 1580-1640 (V&A T.404-1910)
Carpet fragment, Iran, 16th or 17th century (V&A T.30-1956)
Carpet, Iran, 1500-1650 (V&A T.77-1919)
Carpets from 16th-17th century Turkey (V&A 904-1897; T.29-1956; T.348-1920)
Medallion and Animal Carpet , probably Isfahan, c. 1600
The James A. Lucas "Ghirlandaio" Bergama Rug , made in West Anatolia in the 17th century
Knotted pile wool rug (with detail ), Turkey, 17th century
Knotted pile wool rug , Turkey, 17th century
Knotted pile wool rug , Turkey, 17th century