Evening. I've been watching HIMYM since the begining. I've seen every episode at least 3 times and most recently watched the entire series again over winter break. I hope to disprove a number of theories in the community to help boil down the search to the essential facts. Note 1: While it has been noted that Narrorator Ted is an unreliable story-teller all of my assumptions are being made on the idea that he has made edits to his own story for the sake of telling it to his children/censors (Sandwiches = Weed) or correcting mistakes in the telling of the story (the goat incident). If it happened on screen... it happened.
1.0 Robin is not the mother. Let it go.
1.1 In addition to the fact that this is specifically told to you in the very first episode there are those out there that would still hang on to the idea that Robin is the mother. Let me show you specifically why this is incorrect.
1.2 In S03E012 (No Tomorrow) we are shown a woman standing outside the St. Patty party holding a Yellow umbrella. We have specific evidence that tells us that the Mother possesses a yellow umbrella and was at that party. Therefore it would be safe to assume that this woman is infact the future mother of Ted's children.
1.3 In that same episode Robin was across town with Lilly and Marshal finding out that the floors were crooked. There is no way that she could be 2 places at once, therefore Robin is not the mother.
1.4 The term 'Aunt' is used for close family friends. If we are to believe that the evidence presented in the 'present' (2030) is factually accurate 'the children's drawing shown at the end of S03E4 (Little Boys) is real. Therefore the kids know her as Aunt robin. (see also: Name Shifting)
2.0 Victoria, Blah Blah, Talking Girl, Wendy the Waitress, Etc is not the mother.
2.1 We were told in S03E012 (No Tomorrow) that Ted was 'Glad that they had not met that night or she wouldn't have liked (him)'
2.2 Therefore the mother is not a periphial character. We have yet to be introduced to the character as this would make Narrorator Ted's words invalid.
3.0 The mother's name is Tracy... Maybe.
3.1 Back in S01E09 (Belly Full of Turkey) the reaction of the children is one of surprise when Narrator Ted tells the children 'and that was how i met your mother'. This leads to one of two possibilities.
3.2 The children were suprised that their mother was a stripper in her youth and they made the connection because of the name.
3.3 Narrator Ted had not told them the name in the telling and the children were just surprised at his statement.
4.0 The children are his. No doubt about it.
4.1 In episode S01E02 in the first minute of the show the Daughter specifically says "Oh dad".
5.0 Name Shifting and why it doesn't fly.
5.1 In several theories around the web there has been this idea of name shifting and how it could be that if the names were changed around that it would be possible for Robin to be the mother or lilly or something radically different from what exists.
5.2 Name shifting only name the name of the identity of the individual if little is known about the person. It would have to be that the children knew nothing about the person that was their mother for this to be plausible.
5.3 To stretch the idea that the children didn't know that their mother was a TV reporter or a Kindergarden teacher is ludacris. And in fact the evidence presented in the children's drawings prove that 'Aunt Robin' is actually Aunt Robin.
6.0 Then who is the mother?
6.1 The 'Excuse Me' Girl from S03E012 (No Tomorrow) is entirely possible. It fits all the criteria that one needs to be the mother at this point.- At the St. Pattys party- Approximate age of Ted- The brown hair matches that of the childrenNow that being said there I see a major flaw in this theory. It's simply too easy. It locks in an actress to coming back to the show before the storyline is fleshed out. Sitcom writers very rarely write an entire arc years out and i doubt that the mother is being introduced this season.Personally i think 'Excuse me' girl is simply a curve ball to drive the community nuts.
6.2 We haven't met her yet. This is easily the strongest of arguments to be made specifically to the statements made by Narrator Ted. It allows the writers flexibility in their storyline and perhaps never even introduce her until the final episode.
6.3 (Updated 5/4) - From our previous knowledge we know that Stella was at a St. Patties day party- the same one that Ted was at but left early. Presumably she had attened with freinds and one of them left the yellow umbrella. Even though the end of S04E22 gives us an impression otherwise- i'm yet unconvinced that Stella is the mother.
Conclusion: I hope this clears up several community questions. If you have more I will add them to this FAQ- just leave them in the comments. Cheers!