Obviously one who eats non-kosher food does not make a beracha, but what about if the food is kosher but cooked in a non-kosher vessel (one that hasn’t been immersed), or food that was cooked on Shabbos or Yom Tov?
One does not recite a berachah over any food that is not kosher. This includes foods with non-kosher ingredients, and also food that is rabbinically prohibited, or food that is personally prohibited (such as if somebody made a vow not to eat food).
For food that was cooked on Shabbos, the halachah will depend on whether or not it is permitted to eat the food. If the food was cooked for you, then it is not permitted to eat the food, and a berachah would not be made. However, if the food is permitted to eat (the food wasn’t cooked for you, but for somebody else) a berachah would be made.
It is forbidden to cook food in a vessel that was not immersed, but the food remains kosher, and therefore a berachah is made on it.
The laws of making a berachah over non-kosher food are elucidated in Shulchan Aruch, Orach Chaim 196:1, and Mishnah Berurah. Note that for foods that are themselves kosher, but are eaten at a time when it is forbidden to eat (such as a fast day, before Shacharis, before Kiddush, and so on), a berachah is recited (Mateh Efraim 602:24; Daas Torah 271:5).