First and foremost, Yugi sticks with the term of address that someone is comfortable with. If he's too informal, he'll speak more formally to make them comfortable.
Guys his age get [lastname]-kun, with the exception being Kaiba, who's just addressed by his last name with no honorific. Yugi also drops it for Jounouchi, but that's because of the romantic relationship.
Girls his age get [firstname]-chan, though girls he's very close to (such as Anzu and Karasu) are just called by their names straight up if they're okay with it.
Anyone who is actively above him (such as a police officer or an official) or significantly older than him get the typcical respectful address of [lastname]-san.
However, women who are on a similar playing field to him and closer to his age (such as Mai, who was not much older and his equal as a duelist) get [firstname]-san rather than [lastname]-san.
And of course, Yugi uses "Sensei" or [lastname]-sensei for teachers and doctors.
HONORIFIC STYLE
Guys his age get [lastname]-kun, with the exception being Kaiba, who's just addressed by his last name with no honorific. Yugi also drops it for Jounouchi, but that's because of the romantic relationship.
Girls his age get [firstname]-chan, though girls he's very close to (such as Anzu and Karasu) are just called by their names straight up if they're okay with it.
Anyone who is actively above him (such as a police officer or an official) or significantly older than him get the typcical respectful address of [lastname]-san.
However, women who are on a similar playing field to him and closer to his age (such as Mai, who was not much older and his equal as a duelist) get [firstname]-san rather than [lastname]-san.
And of course, Yugi uses "Sensei" or [lastname]-sensei for teachers and doctors.