If my itinerary went something like this:
London
Amsterdam
Paris
Rome
Cinque terre
madrid
Lisbon
I would fly from Paris to Rome and then from Rome to madrid
How many weeks would be recommended?
It depends on what you want to do while there. Can you give us an idea of what you have in mind?
Off the top of my head, a month, minimum.
That would be 3-4 nights in each of the cities, maybe 5-6 days for Cinque Terre (not knowing much about it), travel time, etc.
But like Telemark said, it depends on what you want to do. Plus, you’ll probably want to take a couple days here and there to just lay down in a park somewhere and read a book or something else you hadn’t planned on. Going to all those cities is a lot of making trains and flights and scaring up accommodations and whatnot. It can tire you out.
Two months. A week in each city and a bonus week. But I would also use day trips to check out small towns outside some of those cities. Much easier if you have a secure place to store your pack and just take a small daypack.
Seven years, so you can live for a year in each city. That way you get a real taste for life there, you can learn the language, maybe find a job.
I think you need to be more specific: how long do you have? How much money do you have? What things do you like doing?
The rest of your life. Seriously, where are you living now, that you need to get back to?
I’ll give the lower bounds on time to get everything done/seen in the top 10 lists of To-Dos:
London- 4 days (2)
Amsterdam-3 days (2)
Paris-7 days (4)
Rome-4 days (3)
Cinque terre-2 days (0.5)
madrid-1 day (0.5)
Lisbon-1.5 days (0.5)
and then in parentheses, I put the barest of minimum number of days to really get a feeling of each city and see whether you wanted to ever come back again.
I’d give it at least 4 weeks, my rationale being if you’re going to do the “backpacking around Europe” thing, you might as well do it right. Telling someone “Oh, then I backpacked around Europe for a month” sounds a lot better than “Oh, then I backpacked around Europe for two and a half weeks.” If you can stretch it out to 3 months, so much the better 
My suggestion is to keep your itinerary as open as you’re comfortable with, so if you find that you’re absolutely enchanted with Paris, or if you meet the woman of your dreams in Rome, you can spend some extra time there.
I took just over 3 weeks to do a fairly comparable itinerary, and it wasn’t nearly long enough.
I should have taken twice that. And if I couldn’t have taken the time (I couldn’t), then cut the number of destinations in half.
Just a few minutes to look up each city’s wikipedia page.
I have a serious question though. What exactly does “backpacking” across different cities actually entail? What are you carrying in your backpack, where do you sleep, etc, etc, etc?
I’d say go for as long as you can afford, bearing in mind that you’re probably going to spend more than you think you’re going to. (I’d also say go to fewer countries and more places within each country, unless you’re absolutely sure those are the places you want to go before you die and you know you’re only going to do this once. I mean, why go to Rome and Cinque Terre and not stop off in Florence?)
When I was a young’un, I did a very similar itinerary in a month. If your goal is to “get Europe done with” and cross the major sites off your list, a month is enough time, although it will be rushed and exhausting and you’ll spend a lot of time in transit. I wouldn’t recommend less time, unless it will be your last chance to go to Europe ever or something.
Personally, at this point in my life I’d either double the time of halve the destinations. In my opinion, travel is a lot richer if you have time to make local friends, become a bit of a regular somewhere, time to get bored, and time to wander around aimlessly. I try to stay a week per city when I can.
How old are you? How well travelled are you? Are you more of a “see the sites” person or a “hang around exploring cafes and alleyways” person? Do you like to plan trips extensively, or do you like to go where the wind blows you? What attracts you to a place? Museums? Nightlife? Food? Culture? Adventure?
I did a trip like this when I was young(er). I went solo for 6 weeks through western Europe. It was one of the best things I ever did for myself. Backpacking around Europe is not the same thing as backpacking in the Sierras or the Rockies. You will be sleeping indoors and eating from restaurants and grocery stores, not camping out in the woods (necessarily).
You get an internal frame travel backpack - one where the straps can all be zippered and covered, so it looks and behaves like a regular suitcase or other piece of airline luggage. Some of them have a zip-on day-pack as well, which is handy. You bring enuf clothes for a few days and plan on doing laundry (another chance to meet fellow travelers and locals).
Young people can stay in youth hostels throughout Europe, and most of the world - it is set up for them. You usually give up luxuries at a hostel for a reasonable cost. You get one bed and bunk with others of your same gender and use a communal bathroom/shower/kitchen (if they have one). People traveling this way should always bring a sleep sack (bed sheet sewed together like a sleeping bag). They usually have lockers for security when you are out exploring.
In Europe, at least, most of the travelling is done by train. Young people can get what is called a Eurail pass, which grants them virtually unlimited travel between certain dates.
You can do all this as an old(er) person, too, but you do not get a lot of youth discounts, and you cannot stay in a youth hostel (I think). Ah, to be young again (sigh).
I really like travelling by train. I did the Eurail thing many years ago when I was young. I had no itinerary, just a few things I wanted to see, so I hopped all over the place, and saw a lot of European cities - from Helsinki to Venice. Sometimes I got on a train on a whim… I went from Venice to Amsterdam on the overnight train just to have somewhere to sleep.
Of all the places I visited, I hated Paris. I tried hard to like it, but too many shitty things happened to me there. I have no desire to ever return.
Thanks for all the replies! Im in my mid twenties. Its a trip I want to take after I finish college. The plan would be hostels, over-night trains, and everything I need in a backpack. Ive heard of people cramming it in in 2 Ishmael weeks but I did a mock itinerary and there is no way I could do anything in that time, because of the travel times. So what I’m understanding is that it will take a month at least.
Good for you! I will emphasize the “at least” part. Do yourself a favor and make the most of this opportunity. You are young, in goood health (I presume), have enuf $$ to undertake this trip without hitting the credit card too heavy (I hope), and are otherwise unattached and unemcumbered with responsibilities.
Do this trip on all cylinders, and stay on the road until the money runs out. You can always get a career later. Check back in five years and see how many of the above conditions are still true. Enjoy it while you can!