These are professionals that arrange for the lender/buyer title insurance policy, draw the final documents and legal forms for your loan and/or property transfer, collect all final signatures, transfer funds, and file the legal documents at the court house. The customary professional varies from state to state but they all do basically the same thing.
Selecting the right professional to close your loan and/or handle your real estate transaction will make the difference between a delightfully smooth closing or a night mare that could actually lose the purchase. This is where the rubber meets the road. Everything is approved and all parties agree but if the numbers don't come out right or the paper work isn't correct guess who loses? You do, and so does everyone else that has worked so hard to put it together.
OK, if there is a new loan involved I cannot recommend strong enough that you let the lender/loan officer select the closing professional. (Not you're Real Estate agent. Agents don't do loans) This market is so competitive there is no such thing as "charge less" or "offer a discount". But there is such a thing as experience, competence, knowledge, reliability, commitment, and integrity. Your loan officer will know which companies know how to do FHA/VA or reverse mortgage and are familiar with your lender's documentation requirements.
In some states if the seller is paying closing cost it is customary that he choose the closing company. Keep in mind that is negotiable during the contract process. Few sellers will lose a sale because of the closing company selection. If they will… you need to ask yourself why and maybe you don't really want to buy from him. Builders are an exception to this for obvious reasons.
If you are in a transaction that does not involve outside lenders and you have to select the company this is what you should consider. How many real estate transactions do they handle per month? Is this a side line or a major focus? Are there any conflicting interests? You know what I mean. Common sense tells us that the real estate agent, appraiser, and closing company should not be in any kind of partnership. This is not a joke.