The appraised value dictates the maximum amount you can finance. If you are only putting 3.5% or 5% down, then most likely the answers below are your main options.
However, if you are putting more than that down then as a buyer you could elect to move forward with the transaction and potentially have to pay a higher rate and/or be saddled with additional PMI as opposed to making up the difference out of your pocket.
For example if you were buying a home for $100,000 with $10,000 down payment (10% down) and the home appraised for $95,000. Now your $90,000 mortgage represents a 95% LTV. Your rate would be a little higher due to the LTV and you would pay more in PMI.
As a buyer there are few cases where you would want to pay over the appraised value of the home, but it's an option if you just need to have this particular home.