The gifts are to be given to the Kohen, not transferred in a manner appropriate for sales: Bava Metzia 11b
Giving it to non-Kohanim: Ketuvot 25a
One should not give all of them to one Kohen; this is punished by famine: Eruvin 63a
Rabbinically requiring that certain gifts be given to the Kohen even where they are not required, lest people forget the protocols for giving them: Bechorot 18b
The meat from korbanot
All Kohanim share the meat they are to receive from korbanot on the holidays, and are considered to be part of the weekly Mishmar shift: Moed Katan 17b
Status of these gifts from an animal that is a possible first-born, where the kohen does not receive any sort of substitute as compensation for the lost first-born: Bechorot 18a-b
Status of these gifts if a kohen gives a blemished first-born animal to a non-kohen: Bechorot 18a
Status of these gifts from an animal that is a possible animal tithe: Bechorot 18b
Exempting an animal's owner from these gifts if the animal might have first-born sanctity, lest the owner shear and work the animal: Bechorot 18b