Say a running back who throws the ball up in the air, say 10 yards ahead of himself, and runs and catches it, continues and does a TD. Would that be allowed (my son wonders, and now I too)?
If the QB throws a pass and it’s deflected he can catch it off the deflection. Seen that happen a few times. Also if a player fumbles the ball and it goes into the air they can catch it but that’s not the same as a deliberate pass.
Brett Favre’s very first pass completion was to himself.
So what about the deliberate forward pass to oneself? Is it allowed?
The offense is allowed one forward pass per down and that pass must be made when the passer is behind the line of scrimmage. If you throw when beyond the line of scrimmage or if a forward pass has already been made then it’s a penalty. It doesn’t matter who your intended target is (if anyone), it would be a penalty. Also, if you’re throwing a forward pass then you can’t throw to an ineligible receiver, that’s another penalty.
Of course the referees need to determine if the pass is intentional or if the ball was released by accident, if the latter then it’s ruled a fumble.
I can’t give you a cite, but I’m quite sure no. I’m also sure that at one time (and perhaps still) the quarterback when stationed right behind center is an ineligible receiver. Backs must be one yard behind the line of scrimmage to be eligible. The latter would not affect eligibility after deflection when all offensive players may catch the ball.
Thank you for the replies. So a cunning running back with a safety approching could not throw the ball up in the air, run passed the confused safety, catch it and make a touch down? 
that’s called a forward lateral pass and not allowed
Ah, OK, thanks. Would be fun though.
The same question was asked in one of those “Ask the Official” columns.
So looks like in the NFL it must be a deflected pass for a quarterback to legally catch his own forward pass.
Even if a quarterback could legally toss an “eephus” pass high in the air and race downfield in time to catch it, that sounds like a really stupid play to call.
As I say, the only way the passer could possibly get downfield in time to make the catch would be if the pass was a high lob… which would be easier for defenders to intercept than for the passer to get to. Besides, you wouldn’t want your passer taking the big hit he’d be sure to receive after the catch.
That’s like asking “Could LeBron lob a high pass toward the basket, then run up, catch the ball and dunk it in? And if so, would be get an assist for his own score?” The answer is, “Probably not, but even if he could, why would he?”
In addition to the fact that the pass would have to be tipped for the running back to be a legal receiver on the play (as noted by several), he’d also have to throw it while he was still behind the line of scrimmage. Once the ballcarrier is past the line of scrimmage, any forward pass is an illegal play.
No, it isn’t. There is no such thing as a “forward lateral pass”. A pass is either a forward pass or a lateral.
This is like saying there is no NE direction it is either north or east.
That’s not a relevant comparison. In American football, a pass is either a forward pass, or it’s a lateral (which travels either backwards, or, rarely, parallel to the line of scrimmage). Both sorts of passes are specifically defined in the rules, and those definitions are mutually exclusive. It’s not possible for a forward pass to also be a lateral pass.
https://operations.nfl.com/the-rules/2017-nfl-rulebook/#article-6.-ineligible-receivers
So would a QB in the shotgun be eligible?
I love this, a insight into another realm. Thank you.
Yes, and it’s a play that does get used occasionally – the center either snaps the ball directly to a running back, or the QB hands off or laterals to a running back, and then runs out on a pass route. As defenders usually aren’t looking for the QB to be a receiver, he can often find himself to be open.
It works as a trick play, but teams are generally leery of sending QBs out on pass patterns very often, for risk of injury.
You’re welcome!
Too late to add this in on edit: here’s a video with some examples of such plays: