Not quite in the way of Valentine's Day, but I did once form a hopefully ongoing friendship with someone on a train.

I was on a voyager (pah!) towards Taunton for my first TravelWatch SouthWest meeting there, looking out for people who I'd never met, but who I knew from online would be on that train. Entering a carriage, I saw a chap standing in the aisle, chatting with several other passengers.  As I approached, he looked up and asked, "Sorry, did you want to get past?"

"No", I said: "I think I've found the people I was looking for".

I'd like to think that grahame and I have been friends ever since. 

Although I answered "No" to the poll, I do still remember some people that I met and talked to on long train journeys as a little boy....one, for example, was about the same age as me who I was chatting with in the carriage corridor who "lived on the outskirts of London".....I still even remember his first name.
Even more distant memories are coming back as I write this.  I wonder what happened in their lifes?

This is one of those very rare polls where the important element is not the majority who voted "no" but in the four (and optimistic fifth) who voted "yes" or "not yet". Delighted for you.