Speculation about this has run rampant almost since the show's inception, and it makes sense to an extent. Many television shows kill off major characters in the finale, and this show has made a habit out of not just sticking to the laughs but hitting the emotional notes as well.
Until now, this theory has always had some moments that support it, but others that appeared to invalidate it. For example, in "The Time Travelers," Ted imagines a scenario in which his past self could have an extra 45 days with his wife. Immediately, fans jumped to the conclusion that that must have meant that The Mother was dead, but that's not a confirmation, and Ted referring to The Mother in the present tense several times negated it. Cobie Smulders has said that reading the finale's script made her cry, and the creators of the show (Carter Bays and Craig Thomas) have repeatedly said that it will end with something bittersweet, further teasing the fans that something like this could happen.
With "Vesuvius," there is more evidence to this than ever, and all because of one line of dialogue: "What kind of mother wouldn't be at her daughter's wedding?"
In the episode, this line immediately causes Ted to start crying. Obviously, this has struck a nerve. The Mother apologizes and tries to clarify that she didn't mean to bring up whatever the sore subject is, and Ted knows, so they brush it off and continue on, telling happy stories about Barney stealing his scuba suit.
Instantly, I felt sick to my stomach. This can't possibly mean what I think it means, can it? The Mother can't really be dying from some kind of a terminal illness?! With that, the super-fan in me that identifies greatly with the Ted Mosby character began trying to unravel the mystery and sooth my uneasiness. Sure, it now made sense why she tells Ted that she wants him to not live in the past and that life moves on. Sure, it lines up with how we've never seen The Mother in the 2030 timeline when Ted is telling this story. Yet this show has hinted toward things and given us twists so many times before, and this has to be another. After all, Barney and Robin split up and he was going to marry someone else, yet we're at the wedding now. Marshall may have lost his dad on the same episode everyone was expecting to be an announcement about Lily's pregnancy, but they eventually had baby Marvin, and things weren't as bleak as they could have been. Robin may not be able to have children, but that was already a huge blow and we can't take another like that.
So I present to you an alternative theory, just in case this turns out to be another red herring. The Mother isn't dying at the time of this conversation, nor has she died when Ted is telling his kids the story. This is in reference to Ted's mother, Virginia Mosby.
Luke and Penny at the very least know of Ted's stepfather, Clint, whom Virginia marries in "Home Wreckers"—the episode that also revolves around Ted's future house. Not much is spoken about Virginia in the future, and it could easily be assumed that she's passed on purely due to her age. Ted was born in 1978, making him in his 50s when he begins telling the story. His mother would be in her 70s or older, which doesn't mean that she necessarily has to have died by then, but it's very understandable, and all we know is that she's still alive by Robin and Barney's wedding day. She could very well die the day after the reception.
Ted isn't an only child, as he has a younger sister named Heather. She has only been in one episode of the series so far, "Little Minnesota," where she moves to New York City and Ted becomes overprotective of her. To the best of my knowledge (although if you know otherwise, please indicate so in the comments below), nothing has been thrown out there about Heather being married. In "Single Stamina," he says she once got married for five days, but that's about it, and that really doesn't seem to qualify.
When The Mother asks "what kind of mother wouldn't be at her daughter's wedding?" it is Ted that gets upset, not her. You can write my theory off by saying that The Mother is just self-actualized enough to have come to terms with her impending death more so than Ted and that is why she wasn't upset over going to her daughter's wedding, but that would be playing into the writers' game. Instead, let's say Virginia died before Heather got married. That would be something that naturally meant more to Ted than The Mother, as her mentioning this could make him remember how much he misses his own mom. Maybe this even applies to Virginia dying before Ted marries The Mother and he's simply putting "son" in place of "daughter" in reference to the quote.
Is it a stretch? Possibly. But everything is up for grabs until the finale, "Last Forever," airs March 31, 2014. Even I don't believe it—if I'm honest with myself—but until the show rips my heart out and stomps all over it, I'm going to cling onto hope that I'm not proven wrong. Can someone hand Future Tony a tissue, please?