Sources that discuss reasons for the prohibition on suicide

What are a few (as many as possible) sources in the Gemara and cases in Tanach that deal with why one is not allowed to take his/her own life?

Answer

There is no direct prohibition of suicide in the Bible. The Gemara (Bava Kama 91b) derives its prohibition by exegesis on the verse: "and surely your blood of your lives will I require" (Genesis 9: 5), interpreted as: "I will require your blood if you yourselves shed it."

see also Bereishis Rabba 34:13

There are two famous cases of suicide in Tanach, Saul and Samson:

Saul’s suicide (I Samuel 31: 4-5) is not criticized by Chazal, and on the contrary, the Midrash (34:13) states explicitly that he did not sin, indicating that it was permitted for him to take his own life. Why is this so? The Yam Shel Shlomo suggests two possible reasons.

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  One is that Shaul was concerned that his falling into the hands of the enemy would have provoked the Jewish fighters into an impossible assault against the enemy camp, potentially costing thousands of lives. The Yam Shel Shlomo thus writes that it is permitted to give up one’s life for the purpose of saving other Jewish lives.

  
  


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  Another reason he suggests is that the falling of the anointed King of Israel into enemy hands constitutes a grave desecration of Hashem’s Name, and for this purpose it was permitted for Shaul to take his own life.

  
  


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  A third suggested explanation, which is from the Yefei To’ar (commentary to Midrash) and the Radak (Shmuel 31:4), is that the case of Shaul was special because he had been told by Shmuel that the enemy would not spare his life. Because of the certainty that he would die shortly, and given the special circumstances, it was permitted for him to take his own life.

  
  

Similarly, Shimshon’s suicide (Shoftim 16: 30), in which he brought down a building on himself and his Philistine tormentors, is defended on the grounds that it constituted an act of kiddush Hashem, “sanctification of the Divine Name,” in the face of heathen mockery of the G-d of Israel.

See here, here and there for the sources of the above text and more references.