How many different Hebrew words are there for God?

Answer 1

There is a Jewish tradition that there are 72 names for God, however the "names" on this list aren't actual names. They are based on tradition and numerology.

Here is a list of some of the actual Hebrew names and and titles for God in no particular order (if you can think of some more, add them in another answer):

1. YHVH (יהוה) = God's one true unpronounceable name
   
2. Hashem (ה׳) = a substitute word for God's name, used when not praying
3. Yah (יה) = equivalent to Gosh
4. Adonai (אדוני, יי) = Lord, used to substitute for God's unpronounceable name in prayers
5. Adoshem (ה׳) = Lord, used to substitute for God's unpronounceable name when not praying
6. El (אל) = God or god
7. Eloah (אלוה) = God (related to the Arabic word Allah)
8. Elohim (אלהים) = God (related to the Arabic word Allah)
9. Elokim (אלוקים) = God, used when not praying
10. Elohei Avraham (אלהי אברהם) = God of Abraham
11. Elohei Avoteinu (אלהי אבותינו) = God of our Ancestors
12. Elohei Yisra'el (אלהי ישראל) = God of Israel
13. El Shaddai (אל שדי) = usually translated as God Almighty, but the true meaning is unclear
14. El Ro'i (אל רואי) = God of seeing
15. El Elyon (אל עליון) = Uppermost God
16. El Rachum (אל רחום) = God of Mercy
17. Shechina (שכינה) = God's presence
18. Moshia (מושיע) = Savior
19. Matsilenu (מצילנו) = Our helper
20. Go'el (גואל) Redeemer
21. Hakadosh Baruch Hu = The Holy One Blessed Be He
22. ha-Makom (המקום) = Place
23. ha-Marom (המרום) = High place
24. ha-Rachaman (הרחמן) = The Merciful One
25. ha-Boreh (הבורא) = The Creator
26. ha-Norah (הנוראֽ) = The Awesome One
27. Shamayim (שמיים) = Skies
    
28. Elyon (עליון) = Uppermost
29. Malkenu (מלכנו) = Our King
30. Avinu Malkenu (אבינו מלכנו) = Our Father Our King
31. Shomrenu (שומרנו) = Our Guardian
32. Mechayeh Metim (מחיה מתים) = Lifegiver of the Dead
33. Somech Noflim (סומך נופלים) = Supporter of the Fallen
34. Rofeh Cholim (רופא חולים) = Healer of the Sick
35. Matir Asurim (מתיר אסורים) = Freer of the Captive
36. Ba'al Gevurot (בעל גבורות) = Master of Deeds
37. Rotseh Bitshuvah (רוצה בתשובה) = The One Who Desires us to Return (Literally "Wanter of Return")
38. Adon Olam (אדון עלום) = Lord of the Universe
39. Ribono ha-Olam (ריבונו העולם) = Master of the Universe
40. Dayan ha-Emet (דיין האמת) = The True Judge
41. Oseh Shalom (עושה שולם) = Maker of Peace
42. Ohev Amo Yisra'el (אוהב עמו ישראל) = The One who Loves Israel
43. Ehyeh Asher Ehyeh (אהיה אשר אהיה) = I am who I am
44. Yotser Or (יוצר אור) = Fashioner of Light

Answer 2

There are 72 different titles for HaSHem in the Tanach (Jewish Bible) plus the title 'HaShem'.

Answer 3

There are several Hebrew words used to refer to God, with the most common being Elohim, Adonai, Yahweh, and El Shaddai. Each of these has specific nuances and connotations in Hebrew scripture.