Can you recommend a car GPS for North America and continental Europe?

I have a https://buy.garmin.com/en-US/US/on-the-road/automotive/2013-line/nuvi-2597lmt/prod122521.html. It comes with lifetime map updates, which is nice, and also traffic (which I've never actually used, since my area isn't covered). I've not used it in Eastern Europe, but I did use it in the UK, and it worked fine. I find the lane assist/junction view feature very useful. This is where it shows a rendering or photo of a junction or exit, and shows you the lane you need to be in and also, in select instances, a rendering of what the intersection looks like. Very handy when you are driving by yourself. I also like the size of the screen, much better than using a small smartphone screen when trying to drive. The voice guidance as well is often superior to the google navigation equivalent. I do not like that entering destinations is still awkward (as compared to using something like google maps). This model has voice recognition, which works surprisingly well in a car for things like "Home" or "Find gas station". Also, displaying a list of the directions suffers from bad UI, it's non-intuitive. Finally choosing an alternate route or specifying a specific road is awkward. In order to load European maps, you'll need to buy them separately, but they can be downloaded and installing them on the device is really simple.

Just something to think about. If you have a smartphone, an app like OSMAND may be all you need. http://www.makeuseof.com/tag/osmand-offline-gps-navigation-publish-before-road-trip-article/ Please read the comments...they seem to have included house number search. With OSMAND you download your maps when you have an internet connection (on my phone, it's only via WiFi). From then on you only need the GPS satellites in order to navigate; no internet connection needed while navigating. I bought the paid version (about $7 or $8) and it gives me unlimited map downloads. They have maps for the entire world. Disclaimer: I have an old Garmin NUVI 275T with lifetime maps for both North America and Europe, and use that for actual driving. The one on my smartphone is for walking or as a backup. I am moderately unhappy with the Garmin map updating procedure. It can take hours to update a continent's maps.

Much as I'm a huge OSM fan (and minor contributor), routing using OSM can be challenging. In a recent trip to the UK, OSM routed us by what could only be described as the “scenic route”, down old A roads without bypasses. I wouldn't want to try routing in the US based on the imported TIGER data, because it's old and suspect.

It depends. What do you want from a GPS ? If you have a smart phone, http://copilotgps.com/us/ is a decent turn by turn navigation GPS that has maps worldwide - and it's like 15 dollars. The maps are downloaded and will work without a data connection. I've been using it for years and it works well. If you are backpacking and would like/need need topo maps, an app like http://backcountrynavigator.com/ lets you download topo maps from a variety of sources. Again, it is designed to work without a data connection. It's 15 bucks + any costs for other map sources. In that same vein, http://www.meetearl.com/; the first units of which are shipping soon. It's 350 for the high resolution topo maps but, it includes a FMS/GMRS radio, a shortwave and weather radio receiver, a barometer, anemometer, thermometer, hygrometer, bluetooth and wifi, and a solar panel for charging. If it lives up to its promise it is going to be slick as hell.

IPhone or android phone. They're also useful for other things and they have the most options for different maps and such. I even have marine navigation charts for my iPhone.

I've had several TomToms and like them. They last long enough that my latest one isn't even to be found in their catalog, but http://www.tomtom.com/en_us/products/car-navigation/via-series/via-1605-tm/index.jsp is the closest to my model. They've kept their word about free updates and the maps are good. There's one built in to my France car, and it will take you down all kinds of tiny alleys and get you around a lot of congestion. Smartphone nav is pretty much viable, I use https://play.google.com/store/apps/details?id=com.codesector.maverick.lite on my Nexus 4. Using smartphones as navis is http://www.csmonitor.com/Innovation/2013/0408/California-court-bans-use-of-smart-phone-maps-while-driving unless it's in a mount.

We just use Google Maps on our Android phones for both the US and Europe. It speaks and works perfectly.

For TomTom it looks like you need to https://www.tomtom.com/en_us/shop/maps/. I looked into car GPS systems a couple of years ago and http://www.tomtom.com/en_us/products/car-navigation/go-live-series/go-live-1535-m/index.jsp seemed to have the http://www.pcmag.com/article2/0,2817,2409093,00.asp on the market, but it costs $60/year after the first year.