Is it ok for my baby to sleep with blankets?

No. Babies should be placed in the crib, on their backs, with no blankets, stuffed animals, or other items in the crib. Babies should always be put down on their backs because doing so has been shown to dramatically reduce the risk of sids (sudden infant death syndrome).
Why?? Why does a baby ever need a blanket. If the room temperature is reasonable, the pajamas are warm, i see no need for a blanket. There are safer things to use for comfort.
Yes. Leah -this depends on the age of your baby. Newborns and infants up to 6 months of age should sleep on their backs. You can swaddle your baby in a receiving blanket, or you can use a light blanket made of fabric that is breathable. After 6 months of age, any blanket is fine, as long as you avoid heavy comforters.
Risky business. We lose about 100 infants in the US yearly that suffocate in twisted blankets,against bumpers or tangled in soft toys.If you want to risk it it is certainly a common mistake.But I could never live with myself if something bad happened because of something I did.Once the kid can stand up in his/her crib, they have the skills to avoid this risk.