This is a good topic I've been meaning to ask this. I have read on a lot of books on Gotti. for the most part Gotti ordered many hits but did take part in some. These of some of the hits that I know of that he was involved in.
1973- John, Angelo, and Ralph Galione murdered James Mcbratney. Ralph Galione was the Shooter.
January 1979- Tommy desimone was murdered. There are a few different accounts of who killed him. Some say gotti's crew killed him. Other people say Thomas Agro killed him
1979- Joe Spione- Was the brother-in-law of Desimone. Was killed by the Bergin crew since he knew too much about the Desimone murder
August 1979- Gotti, Angelo, and Willie Boy Johnson murdered Anthony Plate. Tony Plate was a loanshark in Miami who worked for Dellacroce. Supposedly plate was a real psycho and committed murders on behalf of dellacroce. In May of 1979 Neil and Plate were indicted for murder. Neil felt that without Plate he would get off so he ordered Gotti to kill him.
July 1980- Gotti order John Favara's death after he accidently ran over his son Frankie
December 1985- Gotti ordered the deaths of Castellano and Bilotti
June 1986- Gotti ordered death of Robert DiBernardo for badmouthing him
1988- Willie Boy was killed when it was discovered he was an informant
1988- Louie Milito was ordered killed by Gotti
1990- Louie Dobono was ordered killed by Gotti
I'm sure there are others but those are the ones I know of