In no particular order, and in no way to diminish others who have made equally convincing lists, here are the texts (primary sources) that have most influenced my reading of the bible.
1. Enuma Elish: This is great text that details, among other things, the exploits of Tiamut and Marduk. This is one of the ANET that ought to inform any reading of the Hebrew Bible, my work on the divine warfare led me to this text and it completely made me think my rather naive view of the creation myth and the exodus "event".
2. Ugaritic Ba'al Cycle: Like Enuma Elish this text is very important for understanding the gods of the ANE, here the exploits of Yamm and El are detailed, and like Enuma Elish this cycle is key in understanding divine warfare and the exodus event.
3. Galen of Pergamum: On the Passions and Errors of the Soul: This is a key text on the role of the passions written shortly after the time of Paul. This text helped solidify the importance of self mastery and its role in the cultural zeitgeist during and after the time of Paul, not to mention the fact that It is a very entertaining read.
4. Qumran Hymns: Early in my biblical studies education I determined to sit down and read through the dead sea scrolls, it was tedious at times, but the Hymns totally made up for the effort. To this day I often rather mischeviously read, or quote, a hymn in the presence of devote Christians and they always assume that I am reciting one of the Hebrew Psalms...
5. Pseudepigrapha: There are a lot of choice texts in the pseudepigrapha, so if I had to pick just one set of texts I would have to chose the Tales of the Patriarchs (I know I just grouped a bunch of texts together, but it's my list so they are to be considered one text from this point forward :) ). These are key texts in the Sin - Exile - Restoration motif that was present during the Second Temple period.