Some women choose to avoid excessive use of a few specific oils...  

"I chose to avoid daily use of these oils as singles, but did continue to use them when part of a blend as needed throughout my entire healthy pregnancy." - Erica M. 

During Pregnancy:
Basil, Birch, Calamus, Cassia, Cinnamon Bark, Clary Sage (can be used during labor), Hyssop, Idaho Tansy, Lavendin (this is different than Lavender), Rosemary, Sage, Tarragon, and Wintergreen

While Nursing:
If you plan to breastfeed and are concerned about milk production, discontinue regular use of Peppermint a month or two before your due date. Some people are sensitive to mint and have reported decreased milk production when using it regularly while nursing. 

Fennel oil can be used to increase milk supply.  

"I was able to get my milk to come back in for my newborn niece, with capsules of Fennel Vitality oil, 3 years after weaning my son." -Erica M.

For Babies:
Eucalyptus, Basil, Juniper, Peppermint, Hyssop, and Wintergreen should not be used in excess + when used should be kept off the chest/neck/face.  

"I used heavily diluted Thieves under the feet of my newborn son to combat the germs of visiting family + friends." - Erica M.