In Rome, you can buy a 16-Euro pass that works for the whole week on all forms of transport. That’s what I would do if you are there more than a few days. Otherwise, it’s about 1 Euro per ride, on anything (but double-check the latest price).
 
Madrid has the best deal ever – about 6 Euros for a strip of 10 tickets.
 
In Paris, if you are there for long enough and at the right times, get a Carte Orange for about 16 Euros – same deal as Rome for being good on all forms of transport. Otherwise get a carnet of 10 – not sure what that costs. www.ratp.fr
 
In London, get an Oyster or a TravelCard. Do not, not, not buy single travel tickets in all but the most extreme circumstances.  www.thetube.com
 
In Amsterdam, get a strippenkart. Can’t remember the cost.
 
That’s just a few possibilities.
 
Lots of people think they can walk everywhere, which is true to a point, but I think you see a lot more and give yourself a break if you take transport now and then. Don’t worry – you will still be walking 10 miles or so per day without even thinking about it if you’re on the go all day.

Local transportation is usually only a few euros a day — particularly if you take advantage of all day passes, etc. like those mentioned by traveler and are willing to do a fare amount of walking.
 
Taxi’s are almost always VERY expensive, although there are sometimes special set fares from the airport to city center that can be a decent deal if you’re in a group of 2 to 4 — and have enough luggage that you’re willing to pay a little extra to not have to deal with it on the subway.  Otherwise, you’ll probably only want to take a taxi in emergencies — like it’s midnight, it’s raining, you’re not entirely sure how to get from the subway station to your hostel and you’ve sprained your ankle.
 
Admission fees to attractions are sometimes high.  There are museum passes in some cities and countries that will sometimes save money if you’re visiting a lot of attractions in a short period of time — they’re also helpful to save time if there are lines at the ticket windows.
 
In terms of stuff — things are just plain more expensive in Europe because transportation costs and taxes are higher.  I always figure “twice the walmart price.”  If the price tag says $2.00 at Walmart (tax not included in the price) the tag price (which includes all the taxes) in Europe will be the equivalent of $4.00.