What's the best way for a family to travel in Europe - by rail or rental car? We only have two weeks.?

Rail, unless they can learn to drive, the British way.

Compared to US, Europe is small. So so, even if trains are very quick more comfortable and much used than in the US, I tend to think thaht for a family a car is better because it allows to visit the countryside and little villages and not only the main cities.

If you are adventerous, by all means get a rental car. Many of the best vacations happen when you stop at quaint little villages and talk to the locals.
If you are only interested in sightseeing major metropolitan areas (i.e. Paris, Berlin, Milan, Rome,etc), and if you want to avoid the hassle of finding parking spaces and driving through the busiest streets in the world, the rail is a steal. You can buy a ticket for unlimited rail travel for a day, week, or month.

Either way is fine, but I think I would go by car. That way you are on your own schedule. Just know that the driving can be crazy, especially in Paris and throughout Italy. It's fun to drive on the German Autobahn, but it seems like everywhere I go lately there is construcion and that sucks and sometimes you end up just sitting there in a stau (traffic jam)

Europe may be bigger than you think. You can't "do" europe in two weeks. If you want to discover one country then a car is probably best. If you plan to hop from London to Paris to Berlin, to Rome then Vienna (exhausting) then train is probably best.

use a sensible combination of the two, but the most important thing is your itinerary. i spent three weeks in europe last summer with family. we rented a car when it required multiple stops in and around southern france, switzerland and italy and our interests were the things that were a bit off the beaten path. if you plan traveling to mostly cities definitely by train.

gasoline is rather expensive and parking is usually a huge nuisance in most large cities especially near tourist attractions. you will see less on the train in my opinion but have more opportunity to meet and talk with people. so it's a trade off. on the other hand if you are a true blue american and like having a car that works too but will probably require you to stay at bigger more american style hotels away from the central parts of the city.

And do check wether it's the European holiday time when you're travelling. If it is, use the train and book your tickets well beforehand, otherwise you're caught on endless traffic jams!

For many people the decision becomes a financial one. In Europe, especially now, the price of gas is extremely high. That, coupled with the very high tolls on major highways (e.g., France) you might find the group fare offers of the German rail system (Deutsche Bahn) to be worth considering.

Add to that the cost of parking a car in the city center (sometimes as much as $17 for a few hours) to be an added pinch to the wallet.

The train system is efficient, the trains are clean, no hoodlums on the trains, monitored in person and by surveillance camera and the train stations often enjoyable to browse on their own.

Travelling by car across the border (from Germany) to the Czech Republic has been described by some (me included) as completely unenjoyable: the roads are not modern, the trucks are slow, and on arriving: hard to find parking.

I live six months of the year in Europe and have a car but prefer not use it for the above reasons.

Good Luck. Explore these options on the internet and ask questions in fora like these.

I would definitely recommend flying in Europe, too. There are numerous extremely cheap airlines in Europe which connect all the major cities. It is far less time consuming than driving. You can visit many countries and you can always rent a car in the new country. I recommend Ryanair.com, AirBerlin.com, Germanwings.com. Sometimes you can find tickets at Ryanair for less than 1 Euro plus tax. You can't beat that especially because fuel prices are about twice that of Stateside prices. My family lived in Germany for 4 years and did a lot of traveling all overy Europe.