RTM Boy wrote, "I can't think of a single example of serious structural failure and/or decompression that resulted in a mid-air fire. Loss of control, yes. Fire, no", and gave an impressive list of 11 cases.
However, in five of the cases, the fuselage substantially remained connected:
AA 96 (USA 1972) no mid-air fire - landed!
Turkish 981 (France 1974) no mid-air fire
AA 191 (USA 1979) no mid-air fire (despite huge fuel stream from port wing at low altitude) (engine loss and impact damage)
United 811 (over Pacific 1988) no mid-air fire - landed!
El Al 1862 (Netherlands 1992) no mid-air fire (engine loss and impact damage)
The NTSB report records a mid air fire for:
Braniff 250 (USA 1966) 'tumbled down in flames' (to quote Wikipedia)
In the case of Braniff 250, one of the wings was torn off, and the mid-air fire is attributed to the consequent tank rupture.
Wikipedia agrees with the absence of mid-air fire in five cases:
Speedbird 911 (Japan 1966) no mid-air fire
Lake Central 527 [emended from 250] (USA 1967) no mid-air fire - severed at cockpit
BEA 706 (Belgium 1971) no mid-air fire
JAL 123 (Japan 1985) no mid-air fire - notorious for being semicontrollable
China Air 611 (Taiwan 2002) no mid-air fire