Over the counter medications such as adult and children cold medicines, cough meds, ibuprofen, acetaminphen, neosporin, bacitracin, bandages, if you have very young kids teething supplies, diapers and diaper creams, wipes, bath stuff. You might want to consider cloth diapers if you expect tight times. They can be washed and you own them.
Daily stuff like toothpaste, toothbrushes, hair styling products, cosemetics (basics like lipstick, mascara, blush), "ladies monthly" supplies, facial scrubs, lotions, creams or astringents if you use those.
Get a good all purpose cleaner that you can use anywhere from the kitchen counters to the bathroom. Lysol all purpose cleaner or Mr. Clean are good for this purpose. Get it in bulk and some spray bottles...then you can use it for floors, or surfaces. Laundry supplies are important such as detergent, softners, stain removers, and bleach (if you use it).
Last but not least, get your pantry basics stocked up. Dried goods like beans, rice, flour, corn starch, baking powder, baking soda, sugar (white and brown), oats, corn meal, salt, pepper, spices, baking mixes, cooking wines, molasses, (corn syrup if you use it), honey, maple syrup, cooking oil, dried milk, shortening and chocolate chips, dried fruits and nuts. With the basics you'll be able to make anything from scratch.
If you have a deep freezer get meats, breads, make ahead meals are good for future planning. Time savers like instant potato, boxed meals like mac n' cheese and burger helper are nice to have on hand. Canned good basics like soup, broths, meats (tuna and chicken) and veggies and fruits for baking are always good too. Don't go over board because they don't have a long shelf life, but you'd be okay in 6 months time if you stocked up on mayo, salad dressings, and condiments.