This is the cop out answer but he absolutely has to feature on this list. Barclay Goodrow has played in 34 games this season and has a single goal and three helpers for four points. That is not good enough for a Rangers player. His money could be better used on making space for reinforcements at the trade deadline. This isn't to say Goodrow is a bad player, in fact I think he's somewhat underrated by the general fan base because he does the little things well.
Where the issue comes with Goodrow is that he makes $3,641,667 per year against the cap. He's got three years after this season remaining on that deal. This man has four points on the season, for more than $3.5 million. It's not good enough for a team that wants to win the Stanley Cup. While he'll probably find his scoring touch once again when he gets to a new home, the Rangers are desperate for room under the salary cap.
Goodrow has a 15 team no trade list implemented in his deal as well, just to ensure that Rangers are unable to move him. Trying to find a team willing to take him that isn't on that list, or that is on the list that may take him is going to be difficult. Perhaps the Rangers could even find a team that wants his services and could find someone to take him at his current cap hit, albeit that is unlikely. He did win back to back Stanley Cups as a key member of the Tampa Bay Lightning core.
I've seen ideas about sending him back to the San Jose Sharks, where he broke into the league. It's not the worst idea, since the Sharks are enduring a rebuild. They may even be able to get another first round pick for him after they got one from Tampa Bay a few years ago. Although, he was yougner and cheaper at the time, weird things tend to happen in this league.