Yes. You probably own far more than you realize. The cost to replace your clothing, household goods, furniture, and electronics could easily justify the reasonable cost of a renter’s policy. If you are financially independent and living on your own you need protection. Someone could injure themselves in your place or you could accidentally injure someone elsewhere. If you’re at fault, you are financially liable. Considering this could seriously impact you now and your future earnings, it’s just not worth the risk.