The cost of living in Europe is going to be higher than in the US in any event, but Calgrad00 hit the major areas that account for that difference.

Gasoline is heavily taxed, with prices running about $5 to $7 a gallon. But, cars are smaller and fuel efficiency is a big consideration these days. (Besides, there are alternatives to driving in many areas - and public transit is subsidized so as to make it very worthwhile.) Consider, too, that distances driven are much less here.

Food has always been more expensive here in Europe. Part of it is that it's more highly regulated. And it's also really, really good. (More "real" food - without additives and not as highly processed - as my French husband is so fond of saying.)

Taxes are, of course, higher - particularly the VAT which ranges from 15 to 22% in the various countries (and which makes most day-to-day purchases more expensive than in the US). But, in exchange for taxes, there are some genuine services, which kind of makes up for things. Medical care won't cost as much (at least if you're on the local payroll and in the local health care system - on expat packages, they generally maintain your US social security and US based medical insurance).
Cheers,
Bev