I've heard of umbrella policies before and I've seen some questions about them on the site, but I don't know how many assets you need before an umbrella policy is worth it. Does $50K of assets warrant an umbella policy? $100k? $10k? Does it matter if your assets are 401k or primary residence?
Usually they start to make sense when you have assets in excess of $300-500k.
Your homeowner's or renter's policy gives you general liability protection. But once you start needing more than $300k, you may find that using an umbrella policy will save you money versus increasing your homeowner and auto insurance limits. The limits may vary by state.
The cost for the coverage is pretty low. Usually insurance agents are very helpful when talking about this kind of insurance and will help you pick appropriate limits.
I suppose it is the same as any insurance policy. It is warranted when mitigating risk of losing however much you have is worth the cost of the policy to you. Frankly, it is more about how attractive you are to litigants than how much income you have or how protected it is legally. How much you have is a factor, but your potential liability is not limited to the sum of your assets.
Ultimately that is a subjective call that you are going to have to make for yourself.
It comes down to a risk analysis: How much do you have to lose and how likely is that to happen?
Personally, I didn't worry about it until I bought some rental property. At that point, I decided that the risk of being sued went up enough that it made sense, especially considering how cheap it is. I not only have to worry about my tenants suing over something, but any guests they invite over.
Another advantage is that since it is the insurance company's money on the line, they take care of defending it in court. Just saving that hassle, even if you would have won in court without them, may be worth the cost.