In trhe front of a car you have 2 seats. The driver and the passenger.
In the US we often call the passenger seat “shotgun”.
What do you call it?
BTW, why do we call it “shotgun”? It was a term used in the 1800’s for the stagecoaches where you had one man driving the horses and another man sitting next to him holding a shotgun.
Passenger seat.
According to my Aussie wife, ditto.
“I call shotgun” would be understood, due to the influence of American TV, but would be used rarely.
Passenger seat.
Get ready for a shock:
The seat which is occupied by the passenger is called :… the passenger seat.
You see, there are some countries where not everything is about guns. 
“The Front Seat”, which is next to “the Driver’s Seat”.
Passenger seat. Actually, on my previous car, I took it out for a few years. We needed to buy renovation material at times and a Toyota Echo isn’t exactly built for cargo, so I loosened the four bolts and out it came. It made it a hell of a lot easier to haul two-by-fours.
“I call shotgun!”
The passenger seat or the front seat.
Front seat. It is understood to be next to driver’s seat.
In France, besides “the front seat” it is sometimes referred to as “la place du mort”, or dead man’s seat.
If you looked at the owners manual or talked to a dealer the word would be “passenger seat” also. Saying “I call shotgun” is just slang.
That’s funny. Where does it come from?
Passenger seat or front passenger seat.
Unfortunately, the term ‘shotgun’ seems to have been misunderstood in the UK (at least within my immediate circle) - people appear to have misinterpreted the parts of the phrase ‘I call shotgun’ (i.e. “I wish to sit in the front, and I am first to ask”) to the effect that ‘Shotgun’ means the ‘I call’ part.
So, for example, when a box of cakes is offered, someone might say “shotgun the one with sprinkles!” (which makes no sense).
The cars I grew up riding in did not. In fact, neither did the stage coaches.
You grew up riding in stage coaches?
In German we call it “Beifahrersitz” - next-to-driver-seat. 
“Passenger seat”, “Front seat” or “Front passenger seat”.
The term “Riding shotgun” is also understood because - and this may be a shock to Americans - Australia had stagecoaches with armed guards too back in the mid-late 19th century.
As someone mentioned before, the etymolygy of calling “Shotgun!” to bags the front passenger seat (in reference to the old practice of literally sititng next to the driver of a stagecoach with a 12-gauge to guard against bandits or unfriendly natives, in the “shotgun” position) has now evolved to a general term for calling dibs on anything - “Shotgun on the salt & vinegar crisps!”, for example.
Also, just to be extra confusing, to “shotgun” can also refer to an unorthodox method of consuming beer from a can.
Passenger seat. Nobody would have a clue what “shotgun” meant.
(Czech Republic)