What is this wire going from mid-fuselage to the tail on this 737?
It is the HF antenna. It was mostly used in older aircraft, which used them in trans-oceanic flights or in areas without UHF or VHF communications facilities.Modern 737s (and other aircraft in general) have done away with them. On later versions it was fitted in the leading edge of the Vertical fin of B737-200s, as shown in the figure below.



Image from b737.org.uk

Note that these aircraft were delivered in 1982-83. Newer 737s don't have these.