1. Blessing over Non-Kosher food:[1]

A blessing is not to be recited upon eating non Kosher foods or any food that is forbidden in consumption, whether Biblically or Rabbinically. [Practically, this applies even if the food was eaten Beshogeg, nevertheless an after blessing is not to be recited.[2] However, some Poskim[3] rule that a before and after blessing may be recited upon eating Chalav Akum and Bishul Akum, as these are light Rabbinical prohibitions.]

Case of Sakana:[4] One who eats a forbidden food in a case of danger is required to say a before and after blessing over the food as he in truth is eating permitted [food], as he is doing a Mitzvah to save his life, and since he benefits from the food he must therefore say a blessing.

1. Machalei Sakana – Blessing on foods forbidden due to danger:[5]

A blessing is not to be recited over foods which are forbidden to be eaten due to danger. This applies whether the food was prohibited by the Sages due to danger [i.e. fish and meat mixture], or is personally forbidden to the person [i.e. lethally allergic to dairy]. However, if the food is simply generally not healthy or recommended [i.e. high in sugar or salt] then a blessing is to be recited upon eating or drinking the food.  

1. Blessing on food on Yom Kippur:[6]

One who is required to eat on Yom Kippur due to medical reasons [or if he is a child below Bar/Bas Mitzvah] is required to say a blessing before and after eating the foods [if he ate a Kezayis within four minutes, and has the physical and mental capability of doing so[7]].[8] [One who is eating according to Shiurim of less than 30cc and less than 30 grams every nine minutes, is not to say an after blessing at all.]

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[1] Admur 196:1 [regarding Meizid]; 5; 204:15; Seder Birchas Hanehnin 7:9: Michaber 204:9; Piskei Dinim Tzemach Tzedek 7a; Piskeiy Teshuvos 196:1 *Source sheets

[2] Piskei Dinim Tzemach Tzedek 7a

Other opinions: Some Poskim rule that if the nonkosher food was eaten without prior knowledge that it is forbidden, then an after blessing is recited. [Admur 196:1]

[3] Hagahos Rav Akiva Eiger 196; Aruch Hashulchan 196:1; Piskeiy Teshuvos ibid

[4] Seder 7:9; Luach 10:9; Admur 196:5; 204:15; Michaber 196:4 and 204:9; Beis Yosef 204; M”A 204:21; See Piskei Dinim Tzemach Tzedek 7:1; Igeres Hakodesh 26 [it becomes Heter Gamur]; Ketzos Hashulchan 55:7; Likkutei Sichos 3:985 [causes damage to soul]; 19:35

[5] See Michaber 202:4; Seder 7:9; Luach 10:9; Admur 196:5; 204:15; Maharam Shick O.C. 260; Piskeiy Teshuvos 196:1 and footnote 13; Sefer Shemiras Haguf Vihanefesh [Lerner] Mavo Chapter 10 *Source sheets

[6] Seder 7:9 and Luach 10:9 regarding Yom Kippur and Issur food; Admur 618:18 regarding Birchas Hamazon; 196:5 regarding an Issur food and that this applies according to all; 204:15 regarding Yom Kippur and Issur food; Michaber 196:4 and 204:9 regarding Issur; Tur 618 regarding Yom Kippur; M”A 204:21; M”B 604:46; All the following Rishonim regarding Yom Kippur: Maharam Merothenberg 71; Tashbeitz 565; Hagahos Maimanis Brachos 2:2; Rosh, brought in Beis Yosef 618 and Taz 618:1 regarding Birchas Hamazon; Ketzos Hashulchan 55:7

Other opinions: Some Poskim rule that one does not recite a before or after blessing upon eating an Issur even in a case of fatal illness. [Dispute recorded in Taz 618:10; Panim Meiros 2:6, brought in Shaareiy Teshuvah 196:2]

[7] Admur 618:18

[8] The reason: One who eats a forbidden food in a case of danger is required to say a before and after blessing over the food as he in truth is eating permitted [food], as he is doing a Mitzvah to save his life. [Admur 196:5; See Piskei Dinim Tzemach Tzedek 7:1; Likkutei Sichos 3:985; 19:35] The same applies for a sick person who eats on Yom Kippur. A blessing is needed before and after as he has nevertheless benefited from the food despite the fact that he has benefited against his will, and under the duress of his illness. [Admur 204:15]