You'd be surprised what insurance may or may not cover. I practiced as an civil defense lawyer for a couple years and can think of the following situations where insurance didn't cover just off the top of my head:
1) agent pocketed the premium and issued a fake certificate of insurance. This went on for a couple of years and the insured never found out until there was a claim. The agent ended up in prison but that didn't help the insured who was now on the hook for a couple hundred thousand dollars in damages;
2) fire was caused by an electrical short and not covered once the carrier found out there was aluminum wiring. This was an 8 or 12 unit complex and tenants all sued landlord for losing their possessions due to the fire.
3) several cases where the landlord or seller was sued for property code violations under the deceptive trade practices act and the carrier denied coverage as the allegation was of an "intentional act".
4) Insurance won't cover breach of contract claims typically, say you get into a dispute with a contractor the insurance isn't going to cover it but are you going to see it through to trial when your personal assets are at risk in the event you're wrong.
5)Not real estate related but I had another case where I represented one of two partners who were sued for a business deal gone bad. They never formally set up the partnership but one guy was acting through an LLC and my client was acting in the partnership as an individual. Long story short, the partner with the LLC just let a default be entered as his LLC had little to no assets and he had no personal liability. He let the plaintiff execute against what few assets the LLC had and then set up shop a few weeks later under a new LLC. My client had to scrape and claw at a payment plan settlement because his personal assets were at risk if he went to trial and lost.
I look at an LLC as an umbrella policy with a one time fee so long as I keep the paper work straight. I may never need it but its a lot cheaper in the long run just to pay the $400 bucks and not have to worry about it.
The other advantage is that the llc doesn't just shield you from the investment's liabilities but will also shield the investment from your and your other investment's liabilities. Divorces, partnership disputes/lawsuits, deficiency judgments and called loans all can happen more often than you think. The LLC will help you to break your portfolio up into little compartments that are insulated from one another, so if something goes bad with you can can write that part off and have the others largely unaffected. Say you lose a property to a foreclosure with a personal guarantee on the note and the lender takes a deficiency judgment, your other properties are now subject to foreclosure to satisfy the deficiency since they are held in your name. If there were in an LLC they aren't liable for your debts.