I went an entire year in my apartment without taking out a renter's insurance policy. Paying premiums seemed like yet another drain on my already tight budget so I managed to keep putting it off. It was pretty idiotic since replacing all of my stuff if there had been a break-in or a fire would have been a much bigger expense and a huge hassle.
My roommate is a musician with some fairly valuable instruments so insurance was a priority for her, and I agreed to handle it since my mother works at an insurance agency and all. Getting renter's insurance was much cheaper than I'd expected. Our stuff is covered for losses up to $24,000, plus we have $300,000 in liability coverage in case we accidentally catch our house on fire or someone gets injured falling off of our deck, for the low cost of $215 a year. We'll even get a further discount once we get our security system working. The whole process took less than half an hour.
So, seriously, no excuses. If you had to replace everything you owned, that would be a major pain. If you had to pay for everything you owned out of pocket all at once, that would be far, far worse.