Lodging cultures in Europe differ significantly by country, but most people across the continent sleep in hotels. Most medium-sized towns at least have one hotel, and usually have a couple of them in different price ranges. Rooms are generally expensive: they usually go for about €90-300 per night, and prices even exceed that if you're staying in one of the top-end hotels that most major cities have. These hotels usually feature quite some amenities, including a TV, telephone, breakfast, etc. Some countries, such as France, also have roadside hotels that are somewhat similar to motels in the United States.
Because of the relatively high cost of lodging, hostels are popular among younger backpackers. All major cities have them, but they are difficult to find outside the typical tourist places. At around €15-30 per night, hostels are significantly cheaper than hotels. Quality varies widely across the continent. Hostels in eastern Europe are much cheaper and of a much lower quality than those in the western part.
There are also several lodgings of quirky means in which to stay. In Sweden you can sleep in a hotel made completely out of ice; Greece and Turkey have hotels in sandstone or rock caves; and Sveti Stefan in Montenegro is an island village that has been entirely converted into accommodation.