Having covered hotel connections, I would like to discuss auto transportation in the main continent. I can't speak for the British roadways or rails as I haven't been there yet.

Automobiles: Most of the major rental lines are here in Europe and will be more than happy to rent a car with the same guidelines that are in the US. Nobody under the age of 21, higher rates for 21-25 drivers, Ins. ect. There is an interesting note about Italy that my group hasn't been able to figure out. Avis will not allow any Mercedes vehicles in Italy. I believe that it has to do with vandalism or theft but more the latter.
To rent a vehicle you must also have an International Drivers Permit or an International Drivers Liscense (two separate entities). The drivers permit is available state side through AAA for $24 (non-member), and requires (2) passport photos. This is basicly a small booklet that says in about 12 different languages that one of the states in the USA was fooled into thinking you can drive (just kidding) and asks the local government to overlook the fact you have no local drivers license. If you get pulled over or cause an accident, I am not sure what protections you have as they will be determined by the local laws. US govt. protections do not apply so expect the worst.
The International Drivers Liscense is issued through an international racing body or could be through Interpol, I can't remember which. It is a very demanding test for this liscense and most of the ex-pat's over here will have at least looked into getting one. This is also a good first step exam for a racing career so if you know someone who races for a living, ask about it. The Drivers Liscense does give you legal standing in the EU courts of law, the permit may not. The classes and the exam are extreamly tough and considering the state of US drivers, most wouldn't pass even the 2nd time through.
I would like to also note that I have been told about a reciprocating agreement between the state of Utah and Germany. I was told about this by a Utah native resident so it may be urban legend, may not. If you have a Utah drivers liscense, Germany will reciprocate and grant you the same rights of a German Drivers License. I do NOT know what this entails but I am RECOMMENDING you get AT LEAST A PERMIT even if you are from Utah.
Roadways are a difficult thing here in Europe as the lanes can get extreamly narrow and signs can become confusing as there are so many of them. There is a US Army drivers guide that is available on the public server. I will not give out the website as the document does not specificly say "distribution unlimited" but it does exist. I would also recommend getting a car with GPS navagation or a very good navagator with a road atlas.
If you get lost and are using a road atlas in the USA, a GPS is a must in Europe. European atlases are tricky, have numerous ways to designate roadways and not be very complete in my estimation (I don't get lost in the US when using an atlas). A good road atlas to have is the ESSO Road Atlas. It uses consistant map symbols and has the location of every ESSO station in Europe. ExxonMobil likes to know where it's stations are and now you can too. I do not know if BP or RD-Shell have similar products but they probably do.
Finally, to end this little diatribe, fuel prices. If you thought that CalGasoline hitting $3.00 was a milestone, you'll enjoy fueling up here. Diesel still runs at a discount to regular gasoline, or Super in Europe. The current price in my little corner of Germany is 1.09 Euro for diesel and 1.16 for the low grade Super. This is the price in LITERS. A US gallon is 3.78 Liters and the USD is at ~30% discount to the Euro. This translates to prices of $5.36 per US gallon for diesel and $5.70 per gallon for gasoline. Expect to pay about 60 to 75 Euros to go from Empty to Full. Unless you are a group of 4 or 5, it is cheaper to use the trains here in Europe to get from point A to B and it will also save you the hassle of parking. If you have to rent vehicles, just make sure that you factor in the price of fuel.