God says that we must not make images of things that are “with” Him. In Hebrew, the phrase “with Me” is a single word, “iti.” This can also be read “oti,” “of Me.” From this, the Talmud derives that we may not make human images, since people are created in the metaphorical “image” of God (see Rosh Hashana 24b and Avodah Zarah 43b).
The Torah has already cautioned us against making idols; the prohibition here is against making a human form even for decorative purposes. The Shulchan Aruch tells us that an image only violates this prohibition if it is three-dimensional (YD 141:4) and complete (YD 141:7). Though the Talmud prohibits possessing such an object (so that one should not be suspected of idolatry), this is not a concern nowadays. The Shulchan Aruch permits one to own an image of the sun or the moon without fear that others will think he made it. Based on this, the Netziv permits one to own dolls, even though he would prohibit one making them oneself (see Ha'emek She'eila 57:3).
Arguably, our dolls would be okay because they’re generally not “anatomically correct,” though there are those who are stringent to mar a doll or stuffed animal in some way. A full examination of this issue is beyond our scope. Refer to the Maharam of Rutenberg, the Maharit, Rav Elyashiv and Rav Ovadiah Yosef (Halichos Olam). And, as always, consult your rabbi.
This prohibition applies to both men and women, in all times and places. It is #4 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #144 of the 194 negative mitzvos that can be fulfilled today in the Chofetz Chaim’s Sefer HaMitzvos HaKatzar. In the Talmud, it is found in Rosh Hashana 24b, Avodah Zarah 43b and Sanhedrin 7b. In the Shulchan Aruch, it is in Yoreh Deah 141.