Well, if we assume that her and her children's poor health was due to mercury poisoning (her remains were tested in the 20th century and showed high levels of mercury), then if we butterfly that out, their second surviving son, Feodor (Theodore) I, could have been at least a moderate ruler - at the very least, he would not have needed a regent (IOTL, he was mentally retarded). If the relief during the famine of 1601-1603 came directly from a tsar who was also more effective at governing, Poland would have had a much harder time invading.
A MUCH more conservative, less pro-western 18th-19th century Russia, and probably less absolutist. The second is less certain, but autocracy would not have developed in the same way as IOTL.
As a bit of a constitutional Russia wank, perhaps a Zemsky Sobor is called to deal with the famine, and the beginnings of a parliament develop? I admit, it's quite a stretch.
No IOTL Romanov dynasty, that's for sure.