What is a good standard for arrival time to the airport for flights in Europe (for example, London to Rome) and also, flying back from Europe to the United States? Didn't know what to expect as far as security and custom procedures. Thanks for everyone's help in advance.

Your airline(s) will tell you how early you should arrive at the airport. There are variables including the airport.

Two hours minimum; the airline may advise more, which you can find on its website. As well as general security checks entering the airport, the airline is likely to run a second, and sometimes more intense, check at its departure lounge. On trans-Atlantic routes, many airlines want you inside the plane at least a half-hour before stated take-off time and may indeed shut the cabin door well before takeoff.

I usually do 1 hour before flying time in airports I know well for interEurope trips.

I succeeded in 45 min in my local airport. But If I had missed my flight I wouldn't have cared that much.

When I'm not so stupid or disaorganized, I tend to do 1h 30 for inter Europe and at least 2 hours for overseas.
If with the family, I add one hour to be sure.

So all in all, 2 hours for internal, 3 hours for overseas is a good rule.

I do 90 minutes for within Europe and 120 (if business) to 150 (if coach) minutes for trans-atlantic.