Without a doubt Stradivarius violins crafter by Antonio Stradivari in the late 1600's and early 1700's are the most expensive violins in the world.
What is in doubt is which Stradivarius claims the title.
The Lady Tennant
On February 13, 2008 Maxim Viktorov, a Russian businessman and collector, paid a record price for an 18th century violin at a private auction at Sotheby's in London, but the record setting price was not disclosed. It is however estimated at around $7 million USD.
Other expensive Stradivarius':
The Mendelssohn $1.78 million.
The Kreutzer $1.58 million.