Obstacles - I'm worried about jet lag and the
time change!
Jet lag... I can't deny it exists, but in our experience it isn't the giant monster that it is often portrayed to be. If the daylight savings time change throws you for a loop then you will most definitely be affected by hopping over 8 time zones. The question is - how do you minimize the symptoms?
North America -> Europe
When flying to Europe we try and take an evening flight. (Leaving somewhere between 8 and 10 pm is perfect!) After the excitement of getting on the plane and checking out the in-flight movies has worn off it's easier to catch a few hours of sleep when you're already tired to begin with. Some people are excellent plane sleepers, while others find it torturous. In my experience kids are able to sleep on planes easier than adults, as we tend to over-think the situation. Combine over-thinking with being the type of parent who wants/needs to constantly check that the kids are sleeping and comfortable, and that leaves very little time for actual parental shut-eye. Admittedly, the last 2 times we flew to Europe I think I slept a grand total of 45 minutes on each flight. This sounds like a recipe for disaster but it was actually fine; sure, I was tired, but the kids were rested and in good moods and with arriving and getting where we needed to go my brain was able to function as needed. Nothing wakes you up like your first view of the Eiffel Tower - it's better than a shot of espresso! (Okay, the espresso also works well.)
What has also worked well for us in the past (both before kids and with kids) is trying our best to stay up as late as possible the first day we arrive. If you take a late night flight then you'll arrive into Europe in the afternoon, and often by the time you get to your apartment or hotel it will be close to dinner time. Do not be tempted to take a nap! Put your shoes on and get outside… 
walk around your neighborhood and find a nice place to have dinner. If someone falls asleep then let them, but not for very long. If you go to sleep 'for the night' at 4 pm then you'll have a very long day ahead of you when you wake up at midnight and your body thinks it's morning! Try and acclimatize yourself to the new time as soon as possible - and if you absolutely need a nap then have one, but only for 45 minutes. If you arrive early in the morning then a nap will probably be necessary, but try not to sleep for too long during the day or your (already messed up) circadian rhythm will become even more confused. Try and adapt to the new clock as soon as possible; get out, get active, and just ignore your heavy eyelids!
The first few days are tiring, but the excitement of a new place works wonders and getting outside during the day is essential to re-setting your internal clock. Generally within 3 days we are totally on the new time - but we are vigilant with getting to bed 'late' for the first few days. Give clear expectations about what should happen if someone is to wake up in the middle of the night; have some books or an iPod or DVD player that you can put on for a child if they wake up in the middle of the night and you want to keep sleeping. This is when I find having an apartment (as opposed to all staying in one hotel room) essential; having different rooms that people can occupy avoids waking up the entire family.
Don’t plan on accomplishing a lot in the first few days - explore gently and keep your expectations low. You'll most likely suprise yourself and do more than you expected, but keep it realistic.
Europe -> North America
In our experience most flights back to North America leave in the early afternoon. This works both for and against you. The good news is that you usually arrive home close to bedtime; by the time you've made it through your front door and drop your bags you can pretty much head right into your (much appreciated) own bed. The flight is also longer on the way home (darn earth's rotation!), and because it's the middle of the day no one is really tired. We take advantage of the in-flight movies, read, play cards, and eat. By the time we start to get really sleepy the plane is close to landing so an hour or so of sleep may be had if you're lucky. Being able to go to bed soon after you arrive home makes it easier to handle, and again we try our best to jump back into the 'new' time right away. On our last trip we arrived home from Europe on a Sunday night at 8 pm, and the kids had their first day of the new school year on Thursday (4 days later). It was no problem as by then, much to my relief, they were completely back on track. We had some very early mornings for the first few days but quickly acclimatized when faced with 'real life'. Don't be scared off of a European adventure by the fear of jet lag. Yes, it exists, but it's manageable - and worth it!
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