A baseball player's just is typically to hit baseballs or pitch baseballs. There isn't much strategy there with your teammates.
A basketball player's job does rely on teammates, but the skills can translate immediately. If Ray Allen goes to another team, he knows how to hit three point shots.
I don't watch hockey, but I assume that it's something like basketball on ice.
This isn't as easy to do in the NFL, where every player must rely on all of his teammates on the field if he is going to succeed and strategy is paramount. Each team has different playbooks, different strategies, different coaches that yell different things. This is only part of the reason why the NFL trade deadline is boring and should not be expected to bare much fruit for the anxious fan that desperately wants an exciting news story for his team or a shiny new toy for his offense.
Trading for a running back is easier, because there aren't many different ways to run, but there's also not a shortage of free agents or run-blocking schemes that might allow you to be successful without giving up a fourth round pick. Additionally, non-guaranteed contracts allow for teams to just cut a player after the year, rather than have to make a "blockbuster" deal to get rid of the ballooned contracts in baseball and basketball. The NFL doesn't have to operate like that.
So with that being said, Steven Jackson, DeAngelo Williams, LeGarrette Blount, Chris Ivory, Dwayne Bowe, Jared Cook, and basically every other skill player in the league is still with the same team today that he was with yesterday. Mike Thomas was dealt from the Jaguars to the Lions earlier in the week, and Aqib Talib went from Tampa Bay to New England. There ya go.
Jackson and Williams are not likely to remain with their teams after this season. Blount could be released. Bowe would likely be given the franchise tag and then dealt if he is not satisfied with the Chiefs progress, but Kansas City could get even higher value than they would have gotten right now.
There's a reason that MLB Trade Rumors is a very popular baseball site, because baseball makes huge trades all the time. For that same reason, I don't know if NFL Trade Rumors is a site and if it is, it's probably on GeoCities. In the last couple of years, Brandon Lloyd went to the Rams and Marshawn Lynch went to the Seahawks, but there's usually very little news at the deadline. This year was no different.
Now let me go buy that NFL Trade Rumors domain.
Fantasy Take: All players remain where they were, you may carry on.