Verizon user here. Thanks for the info. I have the old phone.

With Verizon, the first question is how new your iPhone is. The Verizon iPhone 4S is what Verizon calls a "world phone" (has GSM built in as well as CDMA), but the Verizon iPhone 4 only had CDMA. Most of the world runs on GSM networks, although some countries also have CDMA.
If you do have a GSM-capable iPhone, you can sign up for an international data and calling plan for just the length of your trip. I am not sure how much that is these days. Alternatively, Verizon will usually unlock your phone on request (unlike ATT). Once unlocked, you can sign up with a local cell plan, including pay-per-use cards. You have to get it unlocked before leaving the US, though, and I think you have to have owned the phone at least 2 months, or some other weird restrictions.
There are still international plans for CDMA-only Verizon phones, it's just that there are fewer countries in which that will be useful.

What about those with Verizon?

Same as PP - I turned the plan off when I returned. I opted for the $24.99 plan but was very cautious about using it outside of wifi so didn't have any problems with overage. I know GPS is a battery hog but not sure about data.

We just went to Egypt in December, and I paid the $25 extra for international data plan. I uploaded pictures and videos almost daily to e-mail back home to family, and surfed quite a bit when away from the hotel (visiting family, etc., where there was no wireless). I never went over the allowed amount, and we were there for 2 weeks.

I agree the SIM card in Europe is the best idea. If it's not possible, the $25 international data plan should be pretty good. You can cancel it immediately upon return. I only paid for one month of it.

I think the ipad is unlocked and can take a GSM SIM card (I know that's true for the current verizon ipad, but I am not positive about the verizon ipad 2). Assuming it is true, I would use the phone on wireless, and then get a sim card for the ipad.

Using maps can use a relatively large amount of data. You can call your phone company (or look online) for past data usage.

If you have completed your two year contract, you can get the phone unlocked and use a SIM from a European provider. If you are still within the contract period, AT&T won't unlock the phone (unless you get really lucky when you ask) and you won't be able to use a local SIM.

buy a sim card when you get over there.

There's so much information out there - can anyone sum it up intelligently?
I have an AT&T iPhone 4 and I'll be in France this summer. I also have an iPad 2 that's set up for Verizon 3G but currently doesn't have a data contract (I think that it has GPS?). I don't care about voice functionality on the phone much, and I can use skype/wifi wherever I'm staying when/if I need to call someone, but I am addicted to using the phone or tablet for maps, directions (don't care about turn-by-turn nav, but like to be able to see if I'm headed the right way), looking up hours and prices, etc. The AT&T website says something like you can add 1)int'l voice and texting for about $25 and 2)you can buy int'l data roaming like this:
$24.99 50 MB Overage: $10/10 MB
$49.99 125 MB Overage: $10/10 MB
$99.99 275 MB Overage: $10/10 MB
......so..... for a two-week vacation, how much data would I use? All advice welcome - thanks!