IMHO: umbrella policies are worthwhile if you have assets that exceed the coverage limits of your primary insurance policy for homeowners (or renters) and (if you own a car) auto.
Some simple examples:
(1) If you are an 18 year old student who rents, has no net worth, and no car, an umbrella policy is unnecessary.
(2) If you are a 45 year old husband-and-wife couple, with two kids of driving age, own three cars (one driven by kids), have $500K in liquid assets and $300K in home equity, you should strongly consider an umbrella policy.
An umbrella policy extends the limits of the underlying primary policies over which it is written. For most ordinary people, that means it is a second layer of insurance over your homeowners and auto policies. An umbrella policy generally requires increasing your primary auto coverage to 250/500 or 300/500. It may require changes to your homeowners policy as well. For auto, umbrella policies generally do not increase UM/UIM limits (if anyone knows of any insurers writing umbrella policies that do provide this coverage, please speak up, I'm interested). Typical umbrella policy limits are $1MM or $2MM.
An excess policy is similar to an umbrella policy, but is written specifically over a single primary layer. Most people will not purchase an excess policy for personal use, and instead, will purchase an umbrella policy.
****READ YOUR POLICY**** It states your rights. My comments do not override your policy; do not rely on what I wrote here, and do not rely on what your insurance agent told you informally. If it's not in your written policy and/or declarations sheet(s), it doesn't matter.