Hi,
As already mentioned, the different countries in Europe have different, seperate operators just as the US and canada have different operators.
However...
> Going to Austria, Italy, Spain & the Greek Isles.
...there is good news:
You can use the same SIM for Austria & Italy:
There is an operator called "3" present in both (and more) countries (drei.at / tre.it). Although the networks are independent, they do not charge roaming.
That means: Get yourself a 3 card in any of their countrys and use it in all 3-countries without additional costs. Bonus: they come pretty cheap.
If you buy it in Austria, 2 plans might be of interest for you:
"ReLoad Extreme":
is a prepaid plan for telephony and data
no frills / no activation fees or anything, activate and buy the "MoreMB"-pack: 100MB for 3,- EUR /month
this is the easiest way because you will really get this SIM in any 3 shop.
If you need a _LOT_ data, then watch out for the following alternatives:
"Internet2go": pay 49,- EUR for a surfstick with 2GB included and 0,02 EUR/MB after that.
The 2 GB / any other traffic you buy later will be valid for 1 year.
Problem: You probably don't need the stick but have to pay for it.
Check out ebay for SIM only.
"Apple ipad-Tarif":
- no activation fee
100MB free upfront.
then 6,- EUR for 2GB or larger plans avilable, but: traffic always only valid for 1 month.
Problem: officially this is only avilable when buying an ipad

What a pity

Check out ebay for SIM only.
Please note that 3 is a rather young company and only has 3G (no 2G) coverage. Thus, the coverage can not keep up with the "old players".
But I am using it regularily when travelling to Italy, Sweden and Austria
I got mine in Austria, use it very often in Italy, Austria and Sweden and pay 0,02 EUR/MB and and I find the coverage good in cities and sufficient outside.
As I said, the advantage for you is that you will have to buy only one SIM for 2 countries. Apart from that you can of course also use any other operator's SIM.
In general, Austria is a pretty cheap GSM market.
Italy is above average pricy (from 20,- EUR up for a 3G data flat)
And I don't know much about spain and greece.
Coverage-wise in general the situation in Europe is _much_ better than in the US, you will hardly find any spot even outside the cities without at least 2G coverage (if you stick to the larger operators unlike 3)
Hope that helped a little and welcome to Europe!
southy