You probably ignored this clause in your lease, and why wouldn't you? If your landlord really required you to buy renters insurance, how would they enforce it? Those who do are glad they did, though. Renters insurance can save your neck even after you leave your apartment building.
Compared with other kinds of insurance (health, car, etc.), renters insurance is super cheap, generally running between $10 and $20 per month. It does protect against all the things it sounds like it should: You can get refunds if a power surge fries all your electronics, or if a sprinkler destroys the carpeting, or if a burglar makes off with your comic book collection.
If those all seem unlikely, perhaps — but that is why you buy insurance. Your plan's protections don't stop at your walls, though. If you lose your laptop, whether through damage or theft, renters insurance can help you fix or replace it. If someone breaks into your car to steal something, renters insurance will cover that too. Perhaps most importantly, if your dog bites someone's ankle (or if that person just slips and falls in your space), renters insurance will cover your personal liability. This includes damage that starts in your apartment and spreads to someone else's, like an overflowing toilet or a kitchen fire.
Even if all your furniture is third-hand from Craigslist, even if you could move with just one box, even if you don't think you own anything nice enough to protect — give renters insurance a shot. For the cost of a Netflix subscription, you could give your future self a huge helping hand.