The best piece of advice I can give regarding saving money in Europe is to travel off-season or at least during "shoulder" season. Hotels and airfares are at their least expensive.  The big crowds will not be there either.   Weather is good in March and April as well as November.

The most expensive part of traveling to Europe are lodging costs.  If traveling with a group of 4 or more, consider saving by renting an apartment.  Don't be afraid to negotiate with the owner for a lower price, but use a reputable North-American based rental agent like http://panacherental.com/  Also, there are lots of good 2 star hotels out there.   I use Eurocheapo.com to find them.

In terms of finding better airfares, check out alternative airports.  For instance, in Italy, try flying into Bologna or Milan then take the train to your destination such as Florence or Rome by train.  Brussels is usually a less expensive airport than any of the Paris options.  The train is about 2 hours from Brussels to Paris.

Always buy the city museum pass.  In Paris, it is called the Paris Museum Pass.  In Rome it is the Roma Pass.   In Florence it is the Firenze Card.    Initially, it might seem these passes cost a lot, but they give no-wait-in-line admission to the best attractions in each city.   Use them for 2-3 attractions per day and they become worthwhile.  Some have transportation options too.

Meals:  I know the food is great but how can you go out every day for breakfast, lunch, and dinner?   Take it easy a few days here and there and grab a sandwich or light meal.   In Italy, seek out enotecas.  They often let you enjoy a full buffet for the cost of a glass of wine.  My favorite is Natalino in Florence.

In Italy, buy train tickets in advance.   For instance, a train ticket from Milan to Rome can be 75 euros on the day of purchase, 19 euros if purchased months in advance.  Use www.trenitalia.com to purchase.