Q: I have an ATT linked iPhone4, and will be traveling in Europe.  I have had ATT unlock my phone, and am planning to buy a SIM card from Vodafone or another European carrier.  With the new SIM, will contacts and apps remain on the phone?

Yes apps stay, yes new phone number, no problem swapping back.

1 Each country has its' own discrete carriers even if name is the same

If you are going to more than one country ,the country you buy a PAYG sim in will immediately switch to roaming as soon as you cross the border to another country

and each sim in each country will have it's own local number

All data remains on the iPhone ,the sim only contains carrier data to allow a connection

see here for list of Apple Approved carriers by country

http://support.apple.com/kb/ht1937

There is no problem switching between carriers, the number comes from the SIM card, not the phone.

What countries are you going to?