The length of your trip is the biggest thing to consider, the longer you stay the more you will need. Once you have factored in the cost of your flights, transport in Europe, visas, insurance etc. How much you need depends on where you travel, Northern Europe is generally more expensive than the East or South, and the bigger cities can be more expensive than smaller towns. Avoiding tourist areas when looking for a restaurant usually allows you to eat well at prices even the locals can afford. Carrying your money safely is important.
Cash is easy but easily stolen and irreplaceable.
Most people carry Traveller's cheques, available at your bank, which you can get in many currencies and amounts. Although you pay a small commission when changing them they are replaceable if lost or stolen. Credit Cards are widely used and often have good exchange rates, but check out the commission charges as they can add up. Discounts are available if you have an Hostels of Europe Card. The Euro was officially launched on the 1st of January 1999.