If you have some fat (75% of westerners are heavily overweight or obese) you can easily fast on water only for weeks, of course you're not going to be able to exercise heavily every day or run a marathon. But if you're an overweight office worker with no other health issues you'll be just fine.
For anything over a week you probably should get medical assistance to keep an eye on vitamins and electrolytes, but you're not going to drop dead/unconscious/destroy your DNA
What's dangerous is starvation, aka fasting until your body starts giving up, but for the average westerner that's going to take a long time.