A Royal Peculiar (or Royal Peculier) is a Church of England parish or church exempt from the jurisdiction of the diocese and the archdiocese in which it lies and subject to the direct jurisdiction of the monarch.

Definition
A “peculiar” is applied to those ecclesiastical districts, parishes, chapels or churches that are outside the jurisdiction of the bishop and archdeacon of the diocese in which they are situated. They include the separate or “peculiar” jurisdiction of the monarch, another archbishop, bishop or the dean and chapter of a cathedral (also, the Knights Templar and the Knights Hospitaller). An Archbishop’s Peculiar is subject to the direct jurisdiction of an archbishop and a Royal Peculiar is subject to the direct jurisdiction of the monarch.

The concept dates from Anglo-Saxon times, when a church could ally itself with the monarch and thereby not be subject to the bishop of the area. Later, it reflected the relationship between the Norman and Plantagenet kings and the English Church. Most peculiars survived the Reformation but, with the exception of Royal Peculiars, were finally abolished during the 19th century by various Acts of Parliament and became subject to the jurisdiction of the diocese in which they were, although a few non-royal peculiars still exist. The majority of Royal Peculiars that remain are situated within the Diocese of London.

Present day

London
The Collegiate Church of St Peter, Westminster commonly known as Westminster Abbey, and containing the Henry VII Chapel which is the Chapel of the Order of the Bath.
The chapels associated with the Chapel Royal, which refers not to a building but to an establishment in the Royal Household; a body of priests and singers to explicitly serve the spiritual needs of the Sovereign. Peculiarly, because the Bishop of London is customarily appointed the Dean of the Chapel Royal, the bishop typically has authority of these chapels as dean, but does not have authority over them as bishop even though they are geographically within the Diocese of London.
The Chapel Royal, St James’s Palace
The Queen’s Chapel, St James’s Palace
The Chapel Royal, Hampton Court
The Chapel of St John the Evangelist in the Tower of London
The Chapel of St Peter ad Vincula in the Tower of London
The Queen’s Chapel of the Savoy, a private chapel of the sovereign in right of the Duchy of Lancaster. It is the Chapel of The Royal Victorian Order. The number of members of the order in recent years has outgrown the available space in the Savoy Chapel so the service for those who have received awards is now held in St George’s Chapel, Windsor Castle every four years.
The Chapel of St Mary Undercroft, the crypt of the former St Stephen’s Chapel in the Palace of Westminster. The building is administered through the Lord Great Chamberlain and Black Rod and it has no dedicated clergy: by convention services were conducted by the Rector of St Margaret’s, Westminster, a member of the Chapter of Westminster Abbey. In 2010, the Speaker of the House of Commons used his right of appointment to nominate an outsider, Rev. Rose Hudson-Wilkin.
The Royal Foundation of St Katharine founded in 1147 by Queen Matilda of England as a religious community and medieval hospital for poor infirm people next to the Tower of London.

Edinburgh
Chapel Royal, Holyrood Palace

Cambridge
The Church of St Edward, King and Martyr, Cambridge

Windsor
St George’s Chapel, Windsor Castle, the Chapel of the Order of the Garter.
Royal Chapel of All Saints (in the grounds of the Royal Lodge in Windsor Great Park)

Former Royal Peculiars
St Michael’s Collegiate Church Penkridge near Wolverhampton
St Michael and All Angels Church Tettenhall Wolverhampton 1247–1548,
Canons of Dover Priory until 1130
Holy Trinity, Minories, London, until 1730
St Mary and St Alkelda, Middleham until 1845
Wimborne Minster 1318–1846
St Peter’s Collegiate Church, Wolverhampton 1479–1846
The Deanery of St Buryan comprising St Buryan’s Church in St Buryan, St Sennen’s Church, Sennen, and St Levan’s Church, St Levan until 1850
The Deanery of Bridgnorth until 1856
Dorchester Abbey 1536–1837
The Collegiate Church & Royal Free Chapel of St Mary the Virgin, St Mary’s Church, Shrewsbury, until 1856
St Mary’s Church, Stafford

Non-royal peculiars
The Peculiar (or Peculier) of Masham
St Mary-le-Bow
Christ Church, Oxford
The Peculiar of Charterhouse
The Parish of Southwick (St James, Southwick and St Nicholas, Boarhunt)
Christ Church, Bath

The following chapels of the Inns of Court are extra-diocesan, and therefore peculiars, but not Royal:

The Peculiar of the Temple Church
The Peculiar of Lincoln’s Inn
The Peculiar of Gray’s Inn

Source from Wikipedia