What is the difference between Mishpatim and Chukim?
Rashi: Mishpatim are Mitzvos that are based on logic, 1 and would therefore have been worthwhile saying even if they had not been said; whereas Chukim are Divine decrees, which the Yeitzer ha'Ra and the Nochrim question as to why we need to carry them out. 2
Ramban and Moshav Zekenim: "Mishpatim" refers to Dinim (the civil laws) listed in Mishpatim, which are the source of communal life and peaceful existence 3 ("Chukim" refers to the Midrashos and "Tishm'ru, to Mishnah - Sifra). 4
Such as the prohibition against stealing, adultery, idolatry, murder and cursing Hashem (Sifra).
Such as the prohibitions against eating Chazir, wearing Sha'atnez and the Mitzvah of Parah Adumah (Rashi) - Chalitzah and Yibum, Taharas Metzora and Sa'ir ha'Mishtale'ach (Sifra).
As the Pasuk indicates a number of times in Yechezkel, chapter 20, and in Nechemyah, 9:29.
Why does the Torah insert the (otherwise superfluous) words "ve'es Chukosai Tishm'ru Laleches bahem"?
Rashi: To teach us that, even if we have learned 'Chochmas Yisrael' (the entire Torah), we have no mandate to study the Chochmos of the Egyptians or of the Babylonians.
Sifra: Refer to 18:4:1:2, and "Laleches bahem" refers to Ma'aseh (carrying out what one learns).
Why does the Torah add "Ani Hashem"?
Rashi: Even though the Chukim are not based on logic and the Yeitzer ha'Ra and the Nochrim want to know why we need to carry them out, the Torah warns us that Hashem issued us the decrees and we have no right to exempt ourselves from performing them.
