Even if you are not thirsty make sure to stop at ALL water stations. Something I have learned from my past marathons is to hydrate whenever possible.
When running longer distances our brain does not always let us know when we are thirsty, or even hungry.
By the time you realize you are thirsty it may be too late (you may be feeling the affects of dehydration).
You do not need to drink the whole cup of water or electrolyte replacement (Power Aid, Gatorade, Nuun, ext.), but take a few sips at each stop.
I have a hard time trying to drink water while running, so I slow my pace to a slow jog while trying to drink. I’ve also found that it helps to kind of pinch the cup to create more of a funnel when drinking (this way less goes down my windpipe!).
It is much better for your body to stay hydrated throughout the race rather than to skip water stations and become dehydrated.
Now when I run a half marathon I do not necessarily stop at every water station. The distance is much shorter so our bodies are not put under as much stress. I would advise you to stop frequently for water or electrolyte replacements though.
Once you finish a marathon (at least for me), I am NOT hungry or thirsty. I know that my body needs refueling so I make sure to drink some form of carbohydrate/protein drink (usually chocolate milk or protein shakes are provides). I also take any electrolyte replacement that is available (usually a bottle of Gatorade).
Lastly, this is more of an etiquette issue, but make sure to stay off to the side when you are drinking your water. Try to check behind you before you stop or slow down to get your water so you do not accidentally cut off another runner or run into anyone.
Don’t worry about throwing your cup on the ground either- you may not always be next to a trash can. I do try to throw it off to the side of the road though if possible. Also be cautious around water station areas, the wet cups can be slippery!