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.
I traveled from Berlin to Warsaw by bus with Ecolines in july 2012.
The bus departures around at 22:00 and it arrives to Warsaw at 6:00 (and it goes on to Lithuania or Kaliningrad).
At around 23:30 we were crossing the German-Polish border. There was nothing. I could see there are still offices or customs point. But no one there.
There's nothing special when crossing border between Poland and Germany. In facts, it may be even hard to notice if you are only a passenger. Nothing special happens on the border.
However, the police controls are intensified near the border. The police can hold you anywhere and control your documents, so you must have your passport (or personal ID, if your'e the EU citizen) with you always when you leave home. But near the border, the controls are more often, and often look like they are made on purpose (the police is expecting someone suspected to travel with given bus - you must give your personal data when buying ticket).
Once I've got 2 police controls for the same bus, middle in the night! All passengers were woken and had to give passports / ID-cards. However, it's hard to give any rule, you can travel 10 times and be never controlled. The bus driver has reacted as if it was nothing special.
Please note, it's not a border control. It's exactly the same as the routine police control when you go to the nearest shop to buy sandwitches.