Regarding recommendations about backpacking and camping in Europe, I would suggest the following:
1) If you can read simple French, then I can highly recommend the FFRP guides. Their website is www.ffrandonnee.fr. The FFRP guides contain both topographical maps (1:50,000) and written trail descriptions, plus information about facilities in the villages, plus some culturel information. The guides are reasonably lightweight and are printed on paper that doesn't dissolve upon exposure to moisture. What's more, these guides are available all over france. Even tiny village grocery stores will have guides for the neighboring trails (though of course Murphy's law says the guide you really want will be out of stock when you get there). There is a map of all the FFRP trails that have guides here. These guides are in French only, so you will have to read French to make full use of them. It is not essential to speak French, though it certainly helps.
Some of the French trails are in the mountains (GR5 in the Alps, GR10 in the Pyrenees) but many are in the lowlands, and thus walkable almost any time of year. I dislike autumn because of the hunters (though French hunters are usually well-behaved), though it is certainly the nice season from a weather point of view. Be prepared for lots of rain in spring time.
France is my favorite country for walking, and it is not really that expensive, contrary to what you hear sometimes. In 2004, for example, I usually paid no more than 30 euro (about $38 at 1.25 $/euro) for a single room, and no more than 10 euro (about $13) for a campground, and nothing when I wild-camped. (To get under 30 euro/night in Paris, you'll probably have to speak fluent French.) Assuming I alternated between these hotels, campgrounds and wild camping, my average lodging would be $17/night. I try to eat at restaurants once a day if possible, and otherwise eat cold food from the grocery store, so that my total costs are under $40/day.
2) If you read Spanish, then there are some good guides to the Spanish side trails in the Pyrenees. I forget the publisher, but you can find them at the big bookstores in Madrid (Libréria Desnivel or Tienda Verde).
Incidentally, neither the French or Spanish Pyrenees are very crowded, other than a few hotspots. They are sort of like Yosemite park in that respect. Yosemite Valley itself is a madhouse, but much of Yosemite park away from the trails is almost empty of humans. Whether in Europe or the United States, most people are not willing to climb several thousand feet with a backpack, just to get away from the crowds near the established trails and huts. If you are willing to do climb high to find a camp, then you can easily have a whole upper valley to yourself in the Pyrenees. In both the Spanish and French Pyrenees, wild camping IS permitted, except in a few specially protected wilderness areas, which together comprise only a small portion of the Pyrenees. And like in said before, wild camping in the lowlands is technical prohibited, but no one cares about hikers or bikers who pitch their tent in a cow pasture or communal forest at dusk and strike it at dawn and DON'T MAKE A FIRE (bivouacing, the French call this). The camping prohibitions are mainly intended for car campers and boy scount types who think camping=campfires.
BTW no one has mentioned the biggest problem with mountain huts. Namely, snoring. This is why I absolutely refuse to sleep in huts anymore. In the Pyrenees, I have sometimes found primitive huts with no other people (and hence no problem with snoring). Alas, these primitive huts tend to have mice. I'd rather be outdoors in the fresh air.
Another possibility in Spain is the Pilgrim's trails that lead to Santiago de Compostela. These are lowland trails where you are expected to stay in refuges in villages each night, though you can also stay in hotels. The primary pilgrim's trail is the Camino Frances in the north. This area is heavily developed so that it is totally impractical to do any camping along this trail. But I camped out along the Camino which goes from Madrid to Sahagun, and also the camino which goes from Seville to Santiago, via Zamora and Ourense. By camping, I mean putting down my bivy and sleeping on a tiny patch of empty ground by the side of a farm road, without even bothering to pitch my tarp. Anything to avoid those snorers in the refuges... There are guides to these caminos at www.csj.org.uk. Because these are lowland trails, you can do them any time of year. If you want to meet lots of other people, these pilgrim's trails are the way to go. There are also pilgrim's trails in France and even German and farther east. (The other pilgrim's trail eventually merge with the Spanish trails.)
One other thing about camping in Europe the way I do. Since I spend much of my time in civilization (restaurants frequently, hotels occasionally) it is very important to keep clean. I always take a daily shower using a 1.5 liter water bottle. The secret is to use only a little soap on the underarms, between the legs and other areas that need soap. There is no need for soap to get rid of dust and salt from the lower legs. Practice this technique at home so you know it like the back of your hand BEFORE you go hiking. Try to be able to finish the bathing in 2 minutes, so you can do it quickly in the bushes by the side of a road while no one is looking. Don't bother with drying off. Just put your clothes back on and burn the water off with body heat. I recommend using liquid soap in a 125ml nalgene bottle. This allows you to dip your finger into the soap and just remove a tiny amount, which reduces the water requirements for rinsing. I wear sandals so my feet don't stink, otherwise you might need soap there. (Yes, I wear sandals in the mountains. Actually, when the going gets really tough, such as a sloped hardpan surface with tiny pebbles, I go barefoot, since barefeet give excellent traction against dry rock.) Also, I wear pure supplex nylon shirt and pants as my base layer (and usually my only layer). Pure supplex is stink-resistant and is easy to clean. If your supplex shirt has that wicking polyester mesh at the shoulders, cut it out. Polyester is a stink-magnet. I avoid tight-fitting base layers of any sort because all such tight-fitting clothing tends to stink. If you absolutely must have a tight-fitting base layer, use merino wool. I made my own supplex shirt and pants to reduce weight by removing pockets and shrinking hems. A clean spare shirt to use for restaurants would also be a good idea. I try to take my daily soap shower in the mid-morning, before going to a restaurant for lunch and while there is sun to dry me out. Then I take a water only rinse before going to bed, to get the salt and dust off my body. I am always careful to carry an extra 1.5L of water for bathing purposes. This adds weight, but is offset by the fact that I don't carry a stove and seldom carry much food.
3) If you read German, there are many nice trails in the Swiss and Austrian Alps. For a great long-distance trail in the Austrian Alps, visit www.arnoweg.com. You can order the guidebook from www.amazon.de using your US credit card, though shipping will run about $20.
4) For those who don't read any foreign languages, Scotland might be the best choice. There was a recent article by Chris Townsend about hiking there here on BLT. I've never hiked in Britain myself.