There have been two separate Blackett baronetcies, only one of which is still in existence. The detailed story of both is outlined in A tale of two baronetcies but the basic facts are follows (title passed to eldest son other than where shown):
BLACKETT BARONETS OF NEWCASTLE
Sir William Blackett, 1st Bt. (1621-1680) was created 1st Baronet Blackett of Newcastle in the County of Northumberland by King Charles II 12 Dec 1673. According to family legend he had made his fortune following a successful transaction in flax, the circumstances of which formed the inspiration for the title of "The Ship That Came Home" by A. W. Purdue, published in 2004. The subject is discussed in detail in an article by Greg Finch.
Sir William's eldest son having predeceased him, the title passed to his 2nd son:
Sir Edward Blackett, 2nd Bt. (1649-1718) Two elder sons having predeceased him, the title passed to his 3rd son:
Sir Edward Blackett, 3rd Bt (1682-1756) Died without issue. The title passed to the eldest son of his brother John Blackett (1683-1750):
Sir Edward Blackett, 4th Bt. (1718-1804) Two elder sons having predeceased him, the title passed to his 3rd son:
Sir William Blackett, 5th Bt. (1758-1816) His eldest son having predeceased him the title passed to his 2nd son:
Sir Edward Blackett, 6th Bt. (1805-1885)
Sir Edward William Blackett, 7th Bt. (1831-1909)
Sir Hugh Douglas Blackett, 8th Bt. (1873-1960)
Sir Charles Douglas Blackett, 9th Bt. (1904-1968) Died without surviving male issue. The title passed to his younger brother:
Sir George William Blackett, 10th Bt. (1906-1994) Died without issue. The title passed to his younger brother (the 3rd son of Sir Hugh Douglas Blackett, 8th Bt.):
Sir Francis Hugh Blackett, 11th Bt. (1907-1995)
Sir Hugh Francis Blackett, 12th Bt. (1955-)
BLACKETT BARONETS OF NEWCASTLE-UPON-TYNE
Sir William Blackett, 1st Bt. (1657-1705) 3rd surviving son of Sir William Blackett, 1st Bt. of Newcastle. In his own right created 1st Baronet Blackett of Newcastle-upon-Tyne in the County of Northumberland by King Charles II 23 Jan 1684/5:
Sir William Blackett, 2nd Bt. (1690-1728) Died without legitimate issue. With his death this baronetcy became extinct, although two of his nephews, Sir Walter Calverley Blackett (1707-1777) and Sir Thomas Wentworth Blackett (1726-1792), successively adopted the name of Blackett under the terms of Sir William Blackett’s will in order to inherit an interest in his estates. Both, however, died without surviving male issue.
The following Blacketts also bore titles:
Sir Basil Phillott Blackett (1882-1935) was created a (non-hereditary) Knight Commander of the Order of the Bath (KCB) in 1921 and Knight Commander of the Star of India (KCSI) in 1926. For brief details of his career please see A Blackett in High Finance.
Sir John Blaket (d. 1430) was knighted by King Henry V after the Battle of Agincourt in 1415. However, no connection between Sir John Blaket and the Blacketts of north-east England has been discovered (see Agincourt and All That).
And finally, Patrick Maynard Stuart Blackett (1897-1974) was created a life peer in 1969 as Baron Blackett of Chelsea in Greater London (see A Nobel Prize for a Blackett).
The fascinating history of the above Blacketts and where they figure in the story of the wider Blackett family is included in more detail in A History of the Blacketts.