Celery does not have negative calories. Although it is theoretically possible for a negative calorie food to exist, none have been identified. A large stalk of celery provides about 10 calories. Only around 2 calories are consumed chewing and digesting a stalk of celery.
Drinking cold water burns a small amount of calories to warm it up to body temperature, but the amount of calories used in this process is minimal. Some chemicals such as caffeine and green tea extract are touted as increasing the metabolic rate. One very small study that compared diet soda drinkers to drinkers of a beverage loaded up with these metabolic boosting ingredients found that the booster drinkers did burn more calories, an effect that might add up to a loss of 10 pounds over the course of a year.