I don't know if this theory has been floated around, but it will consists of two parts - what we know about the mother for now (who she is) and what is the endgame.
I will start from two premises. First: behind every storytelling there is a specific motive. Second: writers don't do anything that is not on purpose.
Information for now: We actually got a fair amount of character information about the mother indirectly. What we know first hand is that she is a musician, had economy classes, liked Love in the time Cholera (Ted's favorite book), has a quirky sense of humor (liked a shellfish joke, for example)
Identity conjecture: Barney's half-sister. Why? First: Barney is being called an uncle. Also: Barney has a half-sister in college. Ted's future wife is in college, as well. However, it is still not conclusive (of course!). First, there is more than one college. Second, Marshall is also called an uncle.
New information: The mother is going to Farhampton train station. She arrived by taxi, and she has to catch a train to city. Previous conjecture possible dispute: Barney's dad doesn't live in a city, so if she is waiting a train to city, it is not likely that she is his daughter (still not conclusive!, we don't know anything about where she is going or where the train goes through). What we know is she was somewhere where she needed a guitar (alternative would be that she is going to somewhere where she needs a guitar, but where would she go at night except home, which suggests the first alternative). Also, the ride was 12.20$. That doesn't seem like much. Also, it shouldn't be dismissed (second premise!). So, where could she have been that takes 12.20$ to Farhampton station and requires a guitar? It is possible that she was playing some music at the wedding. But then, wouldn't Ted have seen her? Here we have a fork
I) She was at the wedding, but Ted didn't see that because of some problems that evidently happened. If she was, it could strengthen half-sister theory (a musician in the family likely wouldn't miss the opportunity to play something at half-brother's wedding)
II) She wasn't at the wedding. That weakens HS theory because why wouldn't a member of the family come to it?
Deciding the fork requires more information, and here I won't go into conjecture.
By the endgame I don't mean what will writers decide to do with episodes of meeting the mother, Ted dating her, etc. I mean it literally - 'what happens in the end'.
Here I invoke my two premises. The second one: nothing is accidental. Example: at one of the reunions in the future, where Marshall is bold, Ted is high and asks: 'Where's my wife?'. I thought nothing of it then.
But think about it, and this is the first premise: every story has a motive. So, take that seemingly random question of Ted's, and ask our own.
Question: Why is Ted telling to kids the story of how he met their mother?
Answer: She died