The other reviewers have laid out much of the characters and the plot for this film, but I wanted to add a couple of things.
This isn't a comedy, but it does have some wry, dry-humour moments as it imitates real-life situations and quandries. It doesn't claim to be a comedy, or a taut spy thriller either for that matter, so if you watch it without expectations, I think you'll enjoy this film.
We think of the past as a simpler time, but this shows it really wasn't. Sure, they didn't have cel phones or laptops or ipods, but if people today are put in the same situation, we'd fare no better than these people. Even today, you could be at a ski lodge or a mountain hotel and the train tracks and roads get snowed over, the snow clearing equipment is elsewhere, the phone lines go down, and because of the mountains, cel reception is non-existent. If the lodge was already full and then had to make room for people stuck because the train isn't going anywhere... you see when I'm going with this.
It doesn't matter if it's 1930 or 2012, when you're stuck, you're stuck. And it's in this setting that we find our characters. They finally board a train and one of them goes missing. The thing is, almost everyone claims they never saw the elderly woman. Who's telling the truth? Who's lying, and, if they are lying, why?
In this arguably timeless film, the female lead is also stuck, so to speak, (a la Flightplan) and begins to doubt her sanity.
Some reviewers may complain about the number of rounds a certain handgun may or may not have, or what Hitchcock should have done differently, but I think this film is fine the way it is. Yes, it's a bit hokey at times, but it does touch on some serious subjects (such as at one point, a country the train enters is in the middle of political turmoil and the train is forceably stopped and everyone on board is afraid they'll be killed) and is timeless. Hence, I would call this film a timeless classic, and, as such, I think anyone who is a Hitchcock fan, a Michael Redgrave fan, an "oldies" fan, or a student of human nature would do well to watch this film.