I'll start off the bat and say everyone who rents should have renter's insurance. It's just a given and it's not very expensive, so look into getting it immediately if you don't have it.
For those of you who've had it for a while, make sure to check in annually to adjust levels and make sure everything's cool. My policy recently renewed and the price went up pretty significantly, so I called my insurance company (USAA) and they told me premiums had increased everywhere, but we reviewed the line items of my policy and found out we could adjust it so that it went down to where it was last year.
For example, I had insured my laptop as an additional asset and since I'm insuring that with my business policy now I didn't need it on the renter's policy. We tweaked a couple of other things too. So make sure to check in with your company, especially if there's a rate hike, and confirm that the policy you have is the one that you need. You may be making more money now than when you set up the policy and are comfortable with a higher deductible that can bring your premium lower, etc. Make sure to ask lots of questions and have them explain the line items to you. Many of them are standard and may be unnecessary to you.
I assume this is the case for car insurance too but there may be less flexibility. I haven't owned a car in years so I don't know. If you have any tips on that feel free to comment.
Fundamental rule of frugality: always be looking for ways to lower your overhead costs!