I know that there is always a passport check when traveling by air. Is that the same case when traveling by train, bus, and car?
Poland is now in the Schengen border-free zone so there should not be any border check at all.
As noted in the comments, you will still need a valid ID to fly, but that is generally true even on domestic flights in Europe. It is purely for the sake of air security. That said, it is always best to have your passport when flying within Schengen as it is the most reliable form of identification in terms of being accepted as such.
As for travel by train or car, there should be no checkpoint (although some Schengen members have begun reinstating some checkpoints, Denmark for example). I've traveled between Prague and Berlin by train and there was no border check.
I travelled from Berlin to Poland (Krakow) by train. I had to provide ID when purchasing the ticket (it was for a Eurail pass), but nothing after that. At the border station (Szczecin), however, I had to switch trains - and there were a few transport police doing spot checks on people. I don't really know why or what they were looking for, but they stopped the Brazilian girl I was travelling with, and not myself - so it seemed fairly random.
Personally if I'm travelling in a country which isn't my own, I always carry my passport.
You can read my blog post on the journey if you want a bit more detail.