There are large European Rental companies (Sixt, Europcar, Maggiore) which have locations in just about every location you may travel. While these companies sometimes offer excellent rates, they tend to sell out faster than non-European companies, and in high season it is possible that these companies may have separate, higher rates for non-EU citizens.
All major U.S. rental car companies offer services throughout Europe, although some have locations only in the most popular of destinations and in the busiest of airports and city centers. If reserving with a U.S. rental company, make sure there are locations where you need them.
Any of the major travel websites can give you a good idea of individual rates and availability. Once you know the rates, use the company website for whichever you select to book as the rates are almost always lower this way. Popular bidding sites can sometimes deliver lower rates if you are either picking up or dropping off a car at a major airport.
Holders of major U.S. credit cards (Visa, Mastercard, American Express) may waive insurance on their rental when paying for the entire rental cost with said card and enjoy free insurance coverage.
Try every company for one-way rental rates, as they vary greatly by season and even date.