Off the top of my head.

Detroit - Abdelkader, Nielsen
Vancouver - Eriksson, Myers
Panthers - Matheson, Bobrovsky
Blackhawks - Seabrook
Islanders - Ladd, Boychuk
Rangers - Staal, Smith, Lundqvist
Buffalo - Skinner, Okposo
Ottawa - Zaitsev, Ryan
Oilers - Neal
Calgary - Lucic
Ducks - Backes

MTL : Alzner
SJ : Vlasic

Im going to consider negative value as someone you would either need to move assets with or retain salary on to move.

Lets see:
Ducks - Backes
Blues - Steen, Bozak
Tampa - I dont think any single player is a negative value here but they might be put there because of their cap situation.
CBJ - You could make an argument for Wennberg but I think they could still get value from him.
Blackhawks - Seabrook, Keith
Preds - Turris

There are more but I'm getting bored

Alright.
Islanders - Ladd, Boychuk, Komarov
Pens - Johnson
Oilers - Neal, Russel
Habs - Alzner and people will hate it but Price
Sharks - Vlasic, Burns, Jones and frankly I don't think anyone takes Karlsson at 11.5 aav either
Canucks - Eriksson, Baertschi
Rangers - Lunqvist
Stars - Another one people are going to hate on but I don't think you take Benn right now at 9.5 aav and his term
Flames - Lucic
Kings - Doughty, Brown, Carter, Quick
Panthers - Bob
Devils - Subban, Scheider
Sabres - Okposo and Sabres fans will complain but sorry boys, Risto is on the list even if you dont want him to be.
Red Wings - just about anyone aged 33 and over on their roster
Sen - Bobby Ryan and Nikita Zaitsev

All of sharks contracts are perfect and have positive value.... lmao
As of today
Vlassic, Jones, Karlsson have really negative vlaue.

Contracts that are Highly probable to end up negative in the near future
Couture in 3-4 years
Kane in 3-4 years
Burns in 2-3 years

Bozak doesn't have negative value. He's not worth much considering his cap hit but they could still get something for him

Nah, with the cap situation the Blues are in noone is taking a 5 mil aav 3C in Bozak without the blues retaining or adding a sweetener.

The same thing was said about Gudbranson last year and the Pens still managed to get a pick. On the other hand, Bozak is a 35-40 points guy with only a year left, a team will surely pay for him. Pure cap dumps like the Steve Mason trade rarely happen

Keith doesnt have negative value. His mistakes are being shown that he can't handle a number 1 role anymore, but if he is on a team where he has another LD to split time with, he is gonna be worth his contract.

IMHO negative value:
In order to facilitate a trade for this player, you would need to add value to the trade more than what you'd get in return.

And for those who get it mixed up: Overpaid and negative value are two different things. Retain 50% on Doughty and every team in the league is asking about him. Loui Ericksson for example even at 50% retained wouldn't be wanted for free. It would still take a draft pick for a team to take him on. That's the difference.