Remembered something from the time when I was working for the railways:
I had a right to grant anyone a right to travel without a ticket, as long as there was a very good an exceptional reason for that. Used it only once, when someone had been robbed and they could prove it. He was let to go to his home, 600 km away, by train for free.
Different countries have different systems, but in Finland it would not be far-fetched to actually hitchhike in a train by politely asking the conductor on the platform before boarding. Just tell about your trip and its goals. Your success rate with that will be maybe 5 %, but it is more than zero!
If you're anyhow at a railway station around the time a suitable train is leaving, it definitely won't hurt to try your luck!
Another thing is that hitchhiking buses is entirely possible as well. Personally, I've done that 3½ times:
- A bus driver somehow told he's "not" going to drive via the locality of Veikkola, and refused to sell me a ticket nor let me enter. I then stopped the next long distance bus on the same stop and asked if his might be the bus I needed. He told it would have indeed been that previous one, and just told me to board his bus. Near Veikkola he stopped on the motorway(!) to let me out the bus. I walked up the ramp and got where I was going.
- In Ukraine it has happened twice that a bus has stopped when I've been hitchhiking with my thumb out. First time the driver made it unambiguously clear that "yes, you are hitchhiking, no, you do not have to pay". The second time we had a similar-ish conversation with the bus driver, but when alighting the bus, I was asked to pay. Which I merrily refused and said byebyes to the driver. I figure that was a misunderstanding, not intentional from by the driver.
- In the Russia I once got a 150 km ride on a 70% full bus. For free.
Especially in buses it should definitely be doable asking the driver if you could hitchhike on his bus. Most will say no, some will say yes. Won't hurt to ask if you're anyway around.
And as a bonus:
With trucks I've done this successfully a lot of times. Even right in the centre of the city, a large truck is bound to be going somewhere far away relatively soon. Sometimes they don't know their next trip yet when you go asking, and can't help. But often the answer is first "no, I'm going nowhere", but if you continue with "but are you maybe going somewhere next morning or something like that?", the answer is often something along the lines of "yes, I'm leaving for this and this town 250 km away at 4:30 in the early morning". And then "why not, actually!" when you ask if you could come by at that time. It does work. (Maybe same could work with bus drivers and train conductors, actually?! Ask where they're going later the same day or tomorrow, and ask if you could join for free!)