Every single conversion syllabus and potential beit din question list asks about Rambam's 13 Principles of Faith. Rambam's list attempts to distill the key ideas of Judaism. If you can not accept these principles, you cannot convert orthodox. I don't know how the other movements stand on these principles, but I was required to know about them for my conservative conversion.
I don't know of a single person who has these memorized, convert or born-Jew. However, you should know this list exists and you should be able to discuss these concepts as being an integral part of Judaism. In other words, while you shouldn't need to memorize them, you should be able to have a conversation with your beit din about these concepts and recognize them as essential to Jewish belief. You should be able to volunteer at least most of them as orthodox beliefs, though not necessarily as a list.
Note: Rambam is also known as Maimonides. Don't confuse him with RambaN, who is also known as Nachmanides. RambaM and RambaN are acronyms. (See Reason #827 You Know You're Crazy: Drowning in Acronyms.)
1. I believe with perfect faith that G-d is the Creator and Ruler of all things. He alone has made, does make, and will make all things.
2. I believe with perfect faith that G-d is One. There is no unity that is in any way like His. He alone is our G-d. He was, He is, and He will be.
3. I believe with perfect faith that G-d does not have a body. Physical concepts do not apply to Him. There is nothing whatsoever that resembles Him at all.
4. I believe with perfect faith that G-d is first and last.
5. I believe with perfect faith that it is only proper to pray to G-d. One may not pray to anyone or anything else.
6. I believe with perfect faith that all the words of the prophets are true.
7. I believe with perfect faith that the prophecy of Moses is absolutely true. He was the chief of all prophets, both before and after Him.
8. I believe with perfect faith that the entire Torah that we now have is that which was given to Moses.
9. I believe with perfect faith that this Torah will not be changed and that there will never be another given by G-d.
10. I believe with perfect faith that G-d knows all of man's deeds and thoughts. It is thus written (Psalm 33:15), "He has molded every heart together, He understands what each one does."
11. I believe with perfect faith that G-d rewards those who keep His commandments and punishes those who transgress Him.
12. I believe with perfect faith in the coming of the Messiah. How long it takes, I will await His coming every day.
13. I believe with perfect faith that the dead will be brought back to life when G-d wills it to happen.
Here is a page that translates Maimonides' 13 Foundations of Judaism at Mesora.org. It states the concepts underlying each of these principles.