is there a limit to the amount of american dollars that can be taken into europe?
I don't know about American dollars taken into Europe but I think that there are American laws on how much you can take out of the country at one time.
For Italy (this is the Italy section so I guessed you're going there) you're required to declare, at Italian customs, if you're bringing into Italy $10,000 or more in currency (any currency, I think). I'm guessing it's the same entry/exit rule for all the countries in the Schengen zone of the EU.
I believe US law also states that you need to declare $10k or more when you leave, Gloria. FYI. (The web site is down atm, or I'd find it for you.)
One does indeed need to declare over $10,000 when entering the US. I once knew someone who didn't declare, was caught by US Customs, spent a year in jail, and is now a felon. I'm not sure what EU law is, but I'm willing to bet that there are similar laws when entering other countries.
I am guessing that $10,000 is probably not a concern for Gloria.