Dehydration is not good. More than just a cramp or headache, you also lose water in your joints which over time can give you problems in your joints, like knee problems.
I keep a water bottle for emergencies on my commute, but usually I just down a big glass of water before I leave and after I arrive because my trip isn't far.
If you do a huge amount of exercise--and I have experienced this on long backpacking or hiking trips--sometimes you can get hyponatremia which is when you lose too much salt. You can tell you have it when no matter how much you drink you can't quench your thirst, especially if you have been consuming gatorade, cliff bars, and basically only sweet things all day. Salty snacks help when this happens.