Plain water contains zero calories. Absorbing it from the gastro-intestinal tract generally costs the body no energy. Why? Just think osmotic pressure.

Excreting any excess water costs the body a little energy, not in pushing the water out, but rather in reabsorbing the solutes in the ultrafiltrate in the kidney's nephrons so that the body does not lose valuable electrolytes together with the water.

Overall, the energy spent on getting rid of excess water is not a lot of energy. Drinking too much water* can have serious effects on your body's electrolyte balance when your homeostatic systems decompensate. Having said this, it is better to err slightly on the side of drinking more rather than less water, especially if you live in an environment where water is not scarce. A good way to tell is by the colour of your urine - if it's concentrated (deep yellow), you should be drinking more water and if it's almost colourless, you can hold back the drinking a little.

* In a healthy normal body, it's actually pretty difficult to drink water to the point that the body decompensates. Most people simply cannot force themselves to drink that much water - more than 20 liters in less than 24 hours for a healthy adult male. It's much easier for someone with cardiac failure or renal failure to overdrink.