I know that there is at least one episode when one player won with $0 -- her name was Mabel (the other 2 whammied out). Were there any other 1- or 2-player $0 winner episodes?
Per Jason Hernandez's awesome episode guides, these are all the (known) $0 winners:
* October 14, 1983 (#020, as Bryce mentioned)
* August 1, 1984 (#225)
* October 22, 1984 (#283, the episode you're thinking of)
* November 26, 1984 (#306, the first three-way $0 tie)
* January 23, 1985 (#347)
* February 4, 1986 (#615, the three-way tie GSN just aired)
* May 8, 1986 (#682)
Out of curiosity: Was there ever an above-$0 tie?
As far as anybody seems to know, no. One nearly happened on June 2, 1986 (#699) after Move One Space was hit on the final spin, but the contestant opted to go for the win...and lost by $1,250.