It is a bad idea to use baby oil with latex condoms, dental dams, gloves, diaphrams, cervical caps, sponges, as well as the protective coatings around some IUDs and any sexual device made of latex. Oil based lubricants can cause break down the latex and make all the methods of contraception mentioned a lot less effective.
If you are on birth control not involving latex (such as the pill) and just want to use baby oil as lube you'd be better off investing in something water based. Oil based lubricants will leave a coating on the vaginal wall that is very hard to get rid of. This increases the chance of bacteria and other infections getting in there and sticking around.
Bottom line is..lube is very cheap, easy to get hold of and is definitely not something to scrimp on...invest in something decent!