What fasts are pregnant women and women right after childbirth obligated to keep?
As always, CYLOR, but I'll copy what the Shulchan Aruch says (as far as I see in 554:5): "Pregnant and nursing women fast on the ninth of Av as they complete the fast on Yom Kipur. On the three other fasts [the seventeenth of Tamuz, the fast of G'dalya, and the tenth of Teves —msh210], they are exempt from fasting. Nonetheless, it is appropriate that they do not eat to enjoy themselves with food: rather, for the upkeep of the child (see also 550:1, above)." Mishna B'rura is silent here.
In 550:1, Shulchan Aruch says "All must fast these four fasts [the ones listed above —msh210] and it is forbidden to 'break the fence'." Rama adds: "However, pregnant and nursing women who are in much pain should not fast. Even if they are not in much pain, they are not required to fast, but their practice is to be stringent. That's specifically for the three fasts, but on the ninth of Av they must complete the fast." Mishna B'rura changes the "should not" (for the much-pain case) to a "must not", and comments: "It seems logical that she's called pregnant from when the baby is noticeable... but perhaps even forty days from conception she's also in the class of 'pregnant' for this if she feels pain. But less than [forty —msh210], it seems she's like any other woman for all rules, unless she's in much pain. And if she feels weak, one should not be stringent on her at all." And on but their practice is to be stringent he comments: "But if they're weak, it seems they should not be stringent. However, even one who needs food should not indulge in meat and wine: just according to his need." (Cf. Marx
In 686:2, Rama says about taanis Ester: "This fast is not a requirement [chova]; therefore, one should be lenient with it at a time of need, like pregnant or nursing women or for a sick person not in danger and even merely those whose eyes hurt that if they are in much pain they should not fast, and repay [the fast on another day —msh210] afterward." Michna B'rura notes the ambiguity: "Pain: this goes on those whose eyes hurt, but a pregnant woman even not in pain does not fast: so writes the Y'shuos Yaakov. The Elya Raba is stringent on this, but for a woman who's given birth in the past thirty days, he, too, is lenient."
I do recommend you don't rely on my translations (or readings) of these sources.
Rav Shternbuch address this question in his tshuvos (http://hebrewbooks.org/pdfpager.aspx?req=19963&st=&pgnum=130) and explains the position of the Brisker Rav that a pregnant woman is essentially a choleh sh'ein bo sakanah, in which case she can eat in amounts less than a shiur if she feels she cannot fast. This holding is also consistent with the Brisker Rav's view that a choleh sh'yesh bo sakanah can eat normally, even on Yom Kippur and is not constrained by eating less than a shiur. R. Shternbuch does caution that he is merely explaining the position of the Brisker Rav but he leaves the psak up to the person's regular rabbi.