Best to just leave it there until you need it.
Part of the great romantic appeal about hitchhiking, particularly across Europe and borders and linguistic and political and cultural divides, is the possibility of getting splendidly and serendipitously lost.
Mind you, this fanciful prospect is the flip side of getting hopelessly and desperately lost and not liking it one bit.
I propose a compromise — bring a phone. A good phone, mind you, with Google Maps. The astute reading this will point out that this isn’t a compromise at all but a complete discarding of the element of risk to which I say not true — the battery might run out. You can fine-tune the serendipity levels by keeping the phone off or not until you need it.
If you live in Europe and you’re hitching to other European countries you already know that roaming costs are extortionate and if you’re coming from North America you’ll find it out soon enough. I have a solution for that, too. Buy a SIM card for every country you’re in. Few and, so far as I know, no countries in Europe don’t have a discount prepay SIM provider from whom you can get a native number over the counter at almost any store.
For between €10 and €20 you can get a SIM with that much credit and if you’re careful how you use it (meaning, just don’t) you’ll have plenty of data credit if and when you need it. This means avoiding the temptation to surf the net while waiting for a ride which requires a degree of self-restraint so elevated that if you manage it you’ll also, as byproduct, achieve nirvana. So you might want to buy a little backup credit when you buy your SIM.
For hiking in the UK, Germany and Spain get a Lebara SIM (one for each country, of course). In the Netherlands get Hema or even one of the mainstream carriers like Orange. In France look for Bouygues (Lebara operates in France, too, but doesn’t offer data). Alternatively, if you’ve got a European postal address you can order a Belgian SIM from the Dutch/Belgian offering Mobile Vikings whose data plan works in both countries and beyond that has very reasonable, non-rapey roaming charges. Note though that Mobile Vikings can’t be bought in stores and can only be topped up online so if you run out of credit and your only way of getting online is your phone then your serendipity risk has obviously somewhat elevated.
A good traveling phone charges quickly and holds its charge for a long time, which means that at this writing there are no good traveling phones on the market. There are a couple of not entirely useless traveling phones, though, and I’m going to recommend the Samsung Galaxy Mini. It’s small, cheap, and durable, it charges reasonably quickly and the user experience is so poor that you’ll be tempted less often to play with it to while away the time between rides.
Remember that Google Maps employs GPS to find your position and GPS uses your battery like its bitch, so use it sparingly. Even if you’ve got plenty of charge the maps application itself is very data intensive so, really, until you need it just try to forget you have a phone.