The general concept is here: https://en.wikipedia.org/wiki/Jus_sanguinis

Croatia: http://eudo-citizenship.eu/NationalDB/docs/CRO%20Law%20on%20...

Section 4: "A child acquires Croatian citizenship by origin: [various criteria about who your parents are]" There's no "may" or "can".

Germany: https://en.wikipedia.org/wiki/German_nationality_law#Descent...

"A person born of a parent with German citizenship at the time of the child's birth is a German citizen. Place of birth is not a factor in citizenship determination based on parentage."

Italy: https://en.wikipedia.org/wiki/Italian_nationality_law#Attrib...

"Italian citizenship is granted by birth through the paternal line, with no limit on the number of generations, or through the maternal line for individuals born after 1 January 1948."

France: https://en.wikipedia.org/wiki/French_nationality_law#French_...

"French citizenship by birth abroad to at least one French citizen The child (legitimate or natural) is French if at least one parent is French."

Some countries (like France) require the birth to be registered, while others do not.

There are literally tens of millions of Americans that are Italian citizens, from their grandfather or great-grandfather, without knowing it.

There are also cases where a US-born may be eligible for other citizenship but must apply. (Ireland, for example, if either parent was Irish.)