In our part of southwestern Connecticut, verbal offers are not considered bona-fide offers, but that isn't necessarily true in all parts of the state, or the country for that matter. Generally speaking, if a buyers agent presents a verbal offer to your agent for your home, and the buyer couldn't even take 15 minutes to write up an offer, I wouldn't hold too much stock in that offer. BUT THERE ARE EXCEPTIONS....
I do want to stress that if your agent receives an offer on your home, whether it's verbal or written, it must be presented to you. As for buyers reading this article, you should know that all offers are to be presented to the seller up until the time of closing, and the fact that you have a fully executed contract on a property does not diminish the listing agent's responsibility to present those offers, unless the seller has specifically requested in writing that they do not wish to see any other bids.
When to respond to a verbal offer: If and when your agent calls you with a verbal offer on your home, it is always your decision as to whether you will respond. Sometimes, the buyer's offer has an odd contingency and the buyers agent might feel that if you won't even consider that offer, that it is not worth anyone's time to put anything formal in writing. It could be that the buyer is out of town and want to move forward and that buyer just can't get together with his/her agent to put an offer in writing. Let your agent be your guide- I can assure you that most listing agents will request that the offer be in writing before presenting anything to you- bu there are extenuating circumstances.
When NOT to respond to a verbal offer: Again, let your agent be your guide. I would tell you to consider not responding to a verbal lowball offer . That buyer has nothing to lose, not even 15 minutes worth of his time to write up an offer. If they are truly interested, the psychological benefits of making a bona-fide offer, along with a deposit check can only help to make that buyer come up to a a reasonable price. If the buyer has not even seen your home, and is purchasing your home for speculation purposes, let him put something in writing.
In some areas, verbal offers are not so frowned upon- ask your agent at the time you authorize your listing contract how verbal offers will be handled.