It's better to have it and not need it, than to need it and not have it.
I am not an attorney; this is not legal advice. Seek appropriate counsel from a competent attorney licensed to practice in your jurisdictions. I am only speaking from personal and professional experience.
An LLC is very adequate in most jurisdictions to protect assets and contain liability. But this depends on a few things. First, treating the LLC properly in its establishment and operation. Have properly setup foundation documents such as operating agreements over and above your basic paperwork. Operate your business like a business. Courts will generally side with good-faith efforts and give the benefit of the doubt if you are trying to do the right thing. If you treat your LLC like a magic wonder-box of liability repellant and do nothing more, then you begin to assume risks inherent with such behavior.
Now, assuming you set everything up correctly and operate your LLC correctly, when can the veil be pierced? Generally you are at risk if you are willfully acting outside reasonable norms (i.e., being willfully negligent) or committing fraud. There is a ton of case law on how this is all determined dating back well over a hundred years. I would strongly advise everyone who is a business owner (LLC or corp) to get familiar with this. You can also have the veil pierced by not following your operating agreements and rules. If you set up an entity to look official, but then don't actually conduct your entity by the rules, courts tend to disregard the entity. If you don't have a clear delineation between your personal funds and your LLC funds, that can be problematic. It goes back to treating an LLC as an official entity rather than as just a shell.
You can also get into trouble by not having any assets actually in the entity. Being an REI and having the property as an asset tends to negate this, but the test is still there and used by the courts - so be aware of it.
In general, as long as you set up the LLC properly, define the rules you will operate it under, actually operate by those rules, fund the LLC commensurate with its operations, and then don't willfully be fraudulent or negligent, you will probably be fine. Again, I can't guarantee anything - I'm not an attorney or other licensed professional to give advice. I just know what's worked for me in other ventures.
All that being said, you will be sued. In the current state of the American mindset, it's a matter of fact. Hopefully it will be just a minor suit, but sometimes it's a big one. Sometimes you can prevent them by being diligent, other times you can't. In either case, you need to have something backing you up.
If you happen to be a multi-millionaire, you have the option of financing your own risk through your available cash and assets. If you don't want to do that or you don't have tens of millions of dollars in liquid assets or cash - then you need insurance.
The catch 22 is that those people in a position to least afford the insurance, need it the most. The beginning investor or business just starting out is very vulnerable to the types of financial hits brought about by law suits. Not even the settlement, but just the defense of a suit can be a killer. Insurance is critical to offer protection.
So how much is enough? As much as your liability exposure. A million sounds like a lot of money to most people but in today's world it's a drop in the bucket. Do some research into verdicts recently in your jurisdiction for negligence or personal injury cases and consider that a low-ball starting point.
But, on the other side of the coin, realize that only about 5% of cases filed actually end up in court. Chances are, your case will settle long before. So what's going to happen in this case?
Let's set up a hypothetical scenario. You have a tenant that falls off a broken stair in your property and cracks their face open. They have scarring that will be visible and will adversely affect their outward appearance. You have insurance in effect for $1 million. You receive a notice from your tenant's attorney that you are being sued for $2 million.
As you get into it and contact your insurance company and your attorney and things start to roll discovery begins, which is where the other side gets your information and you get theirs (basically). They find out that you have a properly set up LLC that holds the investment property valued at say $80k and an account totaling $4,000 in operating captial (wild numbers for example). You also have your $1million insurance policy. Taking all of that information, they know the absolute most they will get in a best case scenario is $1,004,000 plus the property. They offer a settlement number of $1,000,0000, which ironically is the same amount as your insurance policy.
Sometimes the plaintiff will do some probing first, find out about the policy and sue for that amount. Why? It's quick, it's relatively painless for everyone involved, and it's tangible.
If you had no insurance or very little, you run the risk of being held personally liable as it could be construed to be willful negligence that you did not maintain enough insurance to cover your exposure. Or if you had insurance but no LLC then the plaintiff could seize all your assets that were unprotected.
The long and short of my essay is that you have to evaluate the level of risk you want to assume on your own and how much you want to offload to insurance. Then you need to protect your assets in the best way that makes sense.
My day job is in professional services and my partners and I have a very well defined and operated LLC. We weighed it very carefully against what we wanted to do and the pros and cons of the other corporate forms. We spent a ton of cash on setting it up. We also have tens of millions in various liability insurances. Even with all of that, we assume there are some risks. However, we know we've reduced our exposure to all but catastrophic risks.
Just my $.02 on the matter. Above disclaimers are still in effect. I speak only for myself and not for my company, partners, blah, blah, blah.