There should be two dates on your contract; Closing and Possession. Closing is when the deed legally records the property in your name. Possession is when you get keys and have full access. As Kary noted, you should be entitled to the keys no later than 9:00 pm on the possession date. Congratulations on your purchase.
If the purchase and sale says something like "3 days after closing," don't pack your bags quite yet.
If everything goes well and closes on time, you would normally get the keys the same day. Ask your agent about it.