My wife drinks when she is thirsty as do I. My wife drinks a lot of coffee, however. A few times she has gone to the emergency room for unrelated issues (she has shunts) and she has been kept because she is dehydrated. I believe this is her normal state because coffee is a Diuretic (makes her urinate a lot) so she is losing water there and not taking enough in.
I drink when I am thirsty and have never had an issue with dehydration but I don't drink as much coffee.
So I think the answer is "it depends". If you are not normally thirsty for water for whatever reason (drinking the wrong things, not aware, etc...) then only drinking when you are thirsty can lead to dehydration. If you are aware of how much you drink and make sure you drink enough water throughout the day I believe we train our bodies to be thirsty when it needs to be.
Expanding a bit on why only drinking coffee made my wife dehydrated. It has been pointed out that - under normal circumstances - even though you urinate more when you drink coffee you are drinking enough water to not make it matter.
For someone who only drinks coffee, however, they will stop drinking when they have too much caffeine in their system because too much caffeine can cause unwanted side effects such as jitteriness, hypercactivity, headaches, etc... so if they find themselves thirsty they will realize they've had enough coffee to drink and not drink anything. In time, they have trained their thirst to be thirsty for caffeine, not the water the body needs. Such a person can not trust their thirst and so I got into the habit of drinking iced tea with lemon so my wife would start drinking it also getting the water intake she needs and the caffeine intake she desires. I'm happy drinking water when I get thirsty.