I have a TomTom GPS with European maps. I purchased it on Amazon because Best Buy does not carry GPSs with European maps and I did not have time to download them. This GPS already has the European maps installed.
Yes, many rental cars now come with an installed GPS. When I rent my car, they ask if I want a GPS and I decline. If you say "yes" they will charge you for the installed GPS. This way, I have the car GPS, if I want to use it, and my own GPS. On my most recent rental car 4 weeks ago, the installed GPS was hard to figure out and use. Also, I have found that the car's installed GPS has complete maps only for the country that you rent the car in. Maps and directions for other countries is limited--it may not locate a specific address.
As previous posters have mentioned, I also take along a Michelin map. Depending on the settings for the GPS, you may want to take a more scenic route and the GPS may be programmed for a faster (autobahn) route.
If your rental car comes with a GPS, make sure you, or the rental agency attendant, sets the GPS to English.
Without my TomTom GPS, I would not have been able to locate the B&Bs I booked and get around as easily. It is a life saver for me and I won't leave home without it. If you do order one, purchase a dashboard mount and a hard carry case for it. I always take it out of the car and carry it with me. Don't want to attract thieves.