Europe is accessible, interesting and safe. English is widely spoken, especially by the young and travel infrastructure is well developed. With a bit of planning, European backpacking trip will be the experience of a lifetime.
(1) Europe seems small to the Americans, Canadians and Australians, but the short distances are misleading. The density of population and, crucially, the density and variety of cultures is such that what seems like a short hop of two hundred miles might actually have enough to see and experience to take several weeks. You will not see all of Europe during one backpacking trip, so be selective.
(2) Consider the weather and the holiday season when you plan. Check average temperatures and days with sunshine (much better indication of weather than rainfall) when planning where and when to go. In most places there is a clear trade-off between good weather and all attractions being open and prices and crowds. Most Europeans take their main holiday in July and August, which are the hottest months, and this is when school holidays almost invariably fall. Choose more obscure and cooler destinations for the summer months (unless you like hot weather and busy resorts).
(3) Establish a realistic budget. This should include your return tickets to Europe, internal travel, accommodation and daily expenditure. After the return tickets, 40 euro (55 USD at the time of writing) a day is probably the absolute minimum, though it does depend on whether you are travelling alone or with a partner, the means of travel and accommodation choices as well as how much and where you eat and drink out. It might not be enough to cover your travel in Europe.
(4) Consider getting a rail pass if you are going to cover large distances, especially between countries. They are great value, particularly for under 26 year olds. Eurail is for travelers from outside Europe, InterRail is for Europeans (and not valid in your home country). If travelling by train, get yourself the Thomas Cook European Rail Timetable.
(5) Unconventional accommodation options. Although hostels are good value and good company, there are other budget options: in the summer, student residence halls often function as cheap hotels; camping is a realistic possibility (and you can get really cheap gear in the UK or Germany) and in some countries (Scotland, Norway) you can legally camp wild, CouchSurfing is a fantastic option for free accommodation and local knowledge.
(6) Bring a Visa or MasterCard debit card for withdrawing money. All your money should be in a checking account with a 4-digit PIN. Bring a credit card too, especially if you want to hire a car at a major airport, especially in the UK. Visa or MasterCard are best as many places in Europe don't accept AmEx and hardly anywhere accepts Diners. Pre-paid cash cards that replaced travelers' checks are worth having too. Bring some cash – around 100 USD worth - for the first place you land in (pounds for the UK, euros for most other destinations).
(7) Get a good guidebook that covers your route. Rough Guides and Lonely Planets are the best by far and include a phrase book.
(8) Get a map, ideally with public transport information in every big and medium city you visit. Don't rely on free sheets from tourist information offices or hostels.
(9) If you want to save money, don't seek brands and services you know from home, but adapt to the local provision. This is particularly important in Eastern Europe, as many Western branded goods are far more expensive than local equivalents.
(10) If you want to buy any stuff – from camping gear to clothes – do it in the UK, it's cheap and they speak English. Big cities and large supermarkets (ASDA, Tesco) or deep discounters (Aldi: check current offers) are the best value for money.
(11) Bring a GSM cell phone that is unlocked to all networks. If you don't have one, get one cheaply when you arrive. SIM cards are cheap (even free) in many countries in Europe and a phone is very handy for arrangements and bookings. Change a SIM as you move countries as roaming charges can be high.
(12) Make a schedule, but be flexible. Don't try to pack too much in: it's better to spend four days in London and "miss" Oxford than try to cover both in a panting rush.
(13) Give yourself time to recover from any longer journeys, and particularly the inbound flight: jet-lag is a serious reality, and you will need at least a couple of days to take it easy and adapt.
(14) Top cities: London, Edinburgh, Amsterdam, Berlin, Paris, Rome, Athens, Venice, Lisbon, Prague.