I dont have official stats on this one but doing research I've come to the conclusion that Michel Petit was the player who played on the most teams, at 10. He stayed on Vancouver for 5 years, but that was the longest. This also includes going BACK to the same franchise you were once at. Even tough Petit never did that. He was in 10 different cities. Not a good record to be associated with I suppose but he has some company.
Paul Coffey - 9 teams. He should have died an Oiler, but after his holdout in '87 he was never going to be an Oiler again. After '96 he was on five teams for his last five years. Cof was a great player but it makes you wonder if he shouldnt have just packed it up after he was traded from the Red Wings.
Esa Tikkanen - 9 teams. He's also remembered mostly as an Oiler but he was traded or sigend 8 different times. He was on eight nine different teams. Although he returned to NYR twice. All that and yet he still amazingly played in 6 Cup finals.
Anyone have a list of any others. I know I'm missing some, but I dont think there are any who were at 9 teams, and as far as I know definetly not 10.
He played for 7 NHL teams (and 2 WHA teams) from '65 to '80 without a bunch of '90s expansion teams to pad his stats:
1965-66 Toronto Maple Leafs NHL
1966-67 Toronto Maple Leafs NHL
1967-68 Oakland Seals NHL
1968-69 Oakland Seals NHL
1969-70 Oakland Seals NHL
1970-71 California Golden Seals NHL
1971-72 Chicago Blackhawks NHL
1972-73 Chicago Blackhawks NHL
1973-74 Vancouver Canucks NHL
1974-75 Vancouver Canucks NHL
1975-76 Vancouver Canucks NHL
1976-77 Minnesota North Stars NHL
1977-78 Minnesota North Stars NHL
1977-78 Washington Capitals NHL
1978-79 Indianapolis Racers WHA
1978-79 Winnipeg Jets WHA
1979-80 Winnipeg Jets NHL