When can my baby start sleeping in a crib?

As soon as possible. Your baby can sleep in a crib as soon as you bring him/her home. Make sure your baby doesn't sleep on his/her belly.
Any time. A crib is a safe place to sleep for any baby. Some parents prefer a smaller bassinet that can be moved more easily, but honestly from any age a crib is fine if it's convenient to use.
Now. Baby is quite safe in her crib. The earlier she is accustomed to her sleeping area the best for all. If you are breast feeding you might want to move her crib into your room for easy access. To quell your anxiety about baby you might want to install a monitor in her room that will alert to any of your baby's needs. It is unsafe for baby to sleep in the bed while breast feeding or with adults.
From birth. A newborn may sleep in a crib. The crib and items in or attached to the crib should be checked to be sure everything is safe. Remove any items that could smother, choke, or tangle up the baby. Babies should sleep facing up (unless instructed to do otherwise by the doctor).
When you are ready. Babies can sleep in cribs whenever their parents are ready to move them there. Make sure your crib meets federal safety standards and that you do not use or put in bumpers, comforters, blankets, or stuffed animals. And always but your baby on their back to sleep! http://www.Cpsc.Gov/cpscpub/pubs/5030.Html lists the current safety tips for cribs.
When you are ready. People typically keep them in bassinets so they are closer to your bed in your room. Newborns wake up frequently and need to fed. However some babies start sleeping through the night at six weeks and some do a little later. I think decision is based more on convenience. Personally i think 2 months is a good time for transition. Make sure you do not co-sleep and put the baby on back to sleep.
At Once. Your baby can start sleeping in a crib on day 1 ! it is recommended that he/she should be near the parents to make breastfeeding easier, but there is nothing that states a bassinet is required. Also remember that sleeping in bed with the parents is not safe !
As soon as you want. Your baby can sleep in their own crib immediately after birth. Many families choose to have their newborns close to them for the first several months when night feeding is frequent. Your newborn can sleep in a crib, bassinett, or cosleeper immediately. The decision to transition to a crib out of your room is a personal one and your own preferences and needs play a big part in that decision.
Moving to the crib. Babies can sleep in a basinette, crib or approved cosleeper (which attaches to the mothers bed and allows easy access to breastfeed) right from birth. Many parents prefer to have the baby near them at night in the first 3 months, especially if breastfeeding. Moving into a crib around 3-4 months, once night time feeds are fewer and the baby is better at self soothing, usually works well.