Getting passport stamped while driving between countries.

No solid answer to your question. For countries with firm border controls, yes, you will likely get a stamp. However, once you cross over into the Schengen zone, there will be no border checkpoints or stamps. As far as I know, no place to go get them and you would not want a souvenir stamp in your passport.

It's not optional. If the laws of that country say they should stamp it or should not stamped it, that is what happens. The stamp is a legal document, it proves you entered or left the country legally.

Most countries stamp all passports except those of their own citizens, because there is no restriction or time limit on their own citizens staying in the country, but they stamp all foreigners.
EU countries do not stamp passports of any EU citizen, as an EU citizen can stay in any EU country without restriction.

On exception is "passport unions". This means the countries do not have passport checks between them, and agree to have common rules for who is and is not allowed in. The most well known passport union is the Schengen Area. Your passport will be checked (and if necessary stamped) once on entry to the Schengen Area, and once again on exit. Crossing between Schengen Area countries there are no passport checks, nobody to stamp your passport.

On our first trip to Finland, we skied across the Tana River marking the border between Finland and Norway. I was disappointed that there were no border crossing checkpoint for a souvenir passport stamp. Same with the drive back from Kirkenes to Finland, no checkpoint.

Bigger issues in crossing into some countires may be visa requirements. Assuming that you are an American, source of useful travel requirement (e.g. visas) information: https://travel.state.gov/content/travel/en/international-travel.html
For example, if you start in Thailand, you don't need a visa for a short term tourist visit but if you drive from Thialand into Myanmar you will need a visa for Myanmar.

You only get stamps when entering or exiting immigration controlled zones. Since your free to travel within the Schengen zone there will be no stamps in most of Europe. Think of it as traveling between states in the US. Asia is different and there will be immigration check points on entering and leaving. AND the exit stamp is just as important - maybe more so - than the entry stamp.

Maybe you can get your passport stamped if you enter the Republic of Saugeais from France, but I wasn't able to: https://en.wikipedia.org/wiki/Republic_of_Saugeais. See my report: http://mainelywinenews.blogspot.com/search?q=saugeais