I. Halakhic midrashim (or Tannaitic midrashim)
Mekhilta de R. Ishmael — commentary on Exod 12:1-23:19; 31:12-17; 35:1-3.
Sifra (or Torat Kohanim) — commentary on Lev (entire).
Sifre Bemidbar — commentary on Num 5-12; 15; 18-19; 25:1-13; 26:52-31:24; 35:9-34.
Sifre Devarim — commentary on Deut 1:1-30; 3:23-29; 6:4-9; 11:10-26:15; 31:14-32:34.
II. Exegetical midrashim (examples in rough chronological order)
Song of Songs Rabbah
III. Homiletical midrashim (examples in rough chronological order)
Pesiqta de Rav Kahana
Tanhuma-Yelammdenu — extant in two ‘modern’ editions: (1) Tanhuma (Nidpas); (2) Tanhuma Buber
IV. Narrative midrashim (examples in rough chronological order)
Seder ‘Olam (Rabbah)
Pirqe de R. Eliezer
1. The halakhic midrashim, generally speaking, appear to be older than the other groupings. However, the narrative midrashim sometimes exhibit a knowledge of genuinely ancient traditions; it remains unclear just how such material came into their hands. For some ideas, see my article “Exploring the Afterlife of Jewish Pseudepigrapha in Medieval Near Eastern Religious Traditions: Some Initial Soundings,” Journal for the Study of Judaism 30 (1999): 148-77.
2. Note that there is a ‘Rabbah’ for each book of the Torah and for the five festival scrolls (Song of Songs, Ruth, Lamentations, Qohelet [Ecclesiastes], and Esther). This circumstance underscores the connection of midrashic activity with the liturgical cycle of scriptural readings.
3. Exegetical midrashim proceed typically with a verse-by-verse exposition of the biblical book; homiletical midrashim typically discuss only the initial verse(s) of the weekly or festival parashah. Both groups will freely range over the entire Bible, citing verses from Torah, Nevi’im, and/or Ketuvim which advance the course of the exposition.
4. I have by no means provided an exhaustive list of midrashic compositions—only a representative sampling of those which you will encounter most frequently during the course of your readings in the literature of Jewish studies.