Europe has a number of very inexpensive air carriers. Unfortunately, they do not yet operate from Europe to the United States and back, but with they new easing of airspace restrictions this could happen within a few years.
For now, these companies operate very inexpensive flights within Europe, and we use them whenever we can. The newest one of these cut rate airlines is Vueling, www.vueling.com. They call themselves a "New Generation Airline" and for openers they sell one-way tickets from Paris to Milan, Barcelona, Amsterdam, Madrid, Rome, Ibiza, Venise, Valence, and Seville for 30 Euros all taxes included. They also fly from other cities in Europe.
Easy Jet, www.easyjet.com, has been around for a long time and now they also operates cheap car rentals, www.easycar.com, and cheap hotels. It pays to check out their website for all the additional things they offer, like ski packages and other vacation packages within Europe, etc.
There is RyanAir, www.ryanair.com, which is based in London, but flies from Paris to select cities. They ofthen have promotions for 1 Euro per one-way ticket plus tax, about 30 Euros total.
In Germany you can use German Wings, www.germanwings.com to select cities within Europe for very little money. Look for their 1 Euro promotions.
There is also Air Berlin,www.airberlin.com, that flies within Europe. They also quite often offer promotional seats for as little as 1 Euro plus tax for a total of approximtely 19.99 Euros.
Within Italy and some cities in Europe, there is Volare, www.volare.com, but I have never used them.
We have used these cheap air carriers quite a bit. They fly in and out of smaller airports which allows them to keep costs down. If you plan to travel within Europe this might be an inexpensive way to get around, provided you plan in one or two extra days in the city you fly back home from to the States. In my nieces case, the RyanAir flight did not get into Venice so subsequently the flight out of Venice was cancelled. Therefore, she missed her next morning flight back out of Paris to the States. It cost her big bucks... She wound up buying a $1000 ticket out of Venice to get back to the States. She had an AirFrance excursion ticket from Paris back to the States, and AirFrance was of no help whatsoever, and neither was AlItalia in honoring the AirFrance ticket. Had she had the extra day or two, she could have taken the Eurostar train back to Paris..... and still caught her flight from CDG the next day.... Sure, RyanAir reimbursed her for the unused ticket, but that was only $40 versus the $1000 she had to pay to get home.....Well, live and learn....