If someone were to take a survey asking people to list Jewish 'Sages' I would venture to guess that the Rambam (Maimonides) would top that list. Even within the Jewish (religious) world there seems to be a disproportionate amount of shiurim, biographies and overall interest in who the Rambam was and what he held, more so than any other Rishon (even this site has a Rambam tag, and although it also has a Rashi tag I think there are no other tags for other Rishonim). My question is why all the interest n the Rambam specifically?
To understand Rambam's fame, we must first understand the context of which he lived. He was one of the first rishonim, following from the end of the geonim and their period. The academic highlight of Babylonia had died out and the Jews were quickly starting to leave the Iberian peninsula as the Christian rulers made their way into the area. I'd argue that Judaism had a mini crisis during this time period because academia was misplaced once again and the guidance started to disappear.
I can go on about Rambam's philosophical triumphs with his The Guide for the Perplexed and his success as a physician; however, his most important contribution had to be his Mishneh Torah. Now the reason why the MT was such a revolutionary work and why it granted Rambam such fame is because of the mission it had. Until then, practical halacha was very difficult to derive. In order to know the halacha, an individual had to most likely had to either sift through the complicated Gemara, the commentary on the Mishnah, or follow a rabbi's instructions, who in return had to sift through the Gemara and its many commentaries. If Judaism was to maintain its consistency across the Nation of Israel and its many communities, there needed to be a work that compiled all the Laws of the Covenant into a simple, easy to understand set of books that explained what the law is for the Jews. This is similar to the Mishnah, because Yehudah HaNasi wrote and compiled the Oral Law down into his work in order to make sure that Jews did not lose the law in the process of the chaos that ensued after the falling of the Second Temple. The Mishneh Torah plainly listed every single halacha (even those that do not apply anymore) and gave an extensive explanation of it all.
Not only did it compile the halacha, but it did so in a way that avoided personal interpretation. Rather, instead he worked his compilation of the halachot off of a mesorah presented in the Babylonian Talmud. This was revolutionary for its time and would inspire other gedolim afterwards to compile their own works on halacha. Imagine, now one would not need to be a master on the Talmud to know the halacha. Anyone Jew could now learn the halacha that he is obligated to keep, especially since it was written in Hebrew.
This is why Rambam is so famous. He created a revolutionary work, that simplified halacha and made it practical for the masses. He used the mesorah as presented in Gemara as the basis for his work and wrote it in Hebrew so that all Jews could learn from it. Rambam was the Yehudah HaNasi of his day.
I remember Rabbi Berel Wein shlit"a saying that if the Rambam had written any one of his Peirush Hamishnah, Mishneh torah, Moreh Nevuchim - he would have been one of the great sages of our history. Each of them revolutionized its area of the Torah, and is from the most important resources even today. That he wrote all three is beyond belief.
I think it is because Rambam was a big rationalist and probably because Maimonides was a great thinker, perhaps Judaism's greatest thinker in the league of greatest Jewish geniuses such as Albert Einstein. Just as Einstein is the renowned authority of science, so, too, Rambam is considered the most authoritative of Halakhah (Mishneh Torah) and rational thought (Guide).