Here's a testament to how much times have changed: Walter Payton finished with the most career rushing yards at 16,726 upon retiring in 1987. Emmit Smith broke that record in 2002, then finished with 18,355 upon his retirement in 2004.
The closest active running back to the record is Rams running back Steven Jackson, who currently has 9,817. In order for Jackson to break the record, he's going to have to continue averaging his 77.9 yards per game for another seven years.
No disrespect to Jackson, but what are the odds that he plays for another seven years? Even if he does, what are the odds that he gets enough carries in this new pass-heavy NFL where running backs are all but disposable pieces?
Steven Jackson may be the closest to Emmit's record, but one would think that the back with the best chance of catching Emmit is Minnesota's Adrian Peterson, who right now has 7,988 yards rushing in his first six seasons in the NFL.
For him to break the record, he will have to continue averaging his 95.1 yards rushing per game for another six and a half seasons. This does make him more likely to break the record, but again, NFL trends indicate that even this seems to be a long shot.
If a running back has a tremendous day, the single-game yards record could be broken (ironically, Adrian Peterson owns that record with 296 yards against the San Diego Chargers back in 2007).
A running back having a superhuman season and breaking the single-season record of 2,105 yards held by Eric Dickerson is very much in the realm of possibility.
But it takes consistency over a very long period of time (at least a decade) for the career rushing record to fall, and that's something that hasn't been the case for NFL running backs in quite some time.