Dear 100 Hour Board,
This is a lengthy comment for Wisteria on the subject of travelling in Europe (Board Question #47426).
A note about hostels: I've stayed by myself (as a little 19/20 year old girl) in many of the cheapest hostels in London, and never felt unsafe in any of them. The YHA hostels were always more expensive (sometimes considerably so), so I never stayed in them, but I never felt unsafe. (As a testament to my sense of safety, I did feel quite unsafe when I spent the night hiding under a tree with drunk people up the road shouting obscenities at each other.) I've also stayed in (mostly YHA) hostels in Liverpool, Conwy, Lizard, and Penzance, and never felt unsafe in any of them. If you travel with a laptop or other valuables, just be sure that they have somewhere you can lock up your valuables (sometimes the rooms will have lockers, sometimes they'll keep them locked up for you behind the front desk). Use common sense and try to be back to your room at a reasonable hour at night.
A free alternative to a hostel is the train station. I spent one night in Paddington Station, and felt somewhat safe, although it was not particularly comfortable, and I had to share it with all the homeless people from the surrounding vicinity, as well as a security guy (hence the feeling of safety). The train station wouldn't really work comfortably for more than a night - I used it because I was just too cheap to get a hostel for 4 nights instead of 3.
I don't have any travel experience in Europe outside the UK, but I can tell you that if you're planning on travelling to several different cities, you should look into two different modes of transportation: A Eurail train pass, and cheap flights on smaller airlines such as Flybe, Ryanair, and Easyjet. Depending on where you are planning to travel/how many stops you want to make, one will be cheaper than the other, but those are probably your best options. Also, if you plan to travel between major cities in the UK, look into National Express FunFares (London - Cardiff for £1 is my favourite!). An upside to travelling by train is that trains will usually drop you off in the centre of the city, whereas those cheap little airlines might fly you into an airport 20 miles outside the city, so you'll have to factor in the cost of travel from airport to city. The smaller airlines also have rather stringent (and stingy) luggage restrictions.
When you go sightseeing, try to heavily balance out the sites that you pay for with activities that are free. Even some places that cost are free at times. You can get into Westminster Abbey for free at evensong, for example, and I've seen some museums that were randomly free on particular days of the week. Also, if you're a student, it might be worth the investment for you to get an International Student Identity Card (ISIC), which will often get you discounts on admission to places or even on train fares. Always ask for a student discount (and try to look and act like a poor student rather than a rich American).
Don't buy expensive souvenirs; take pictures instead. Or just enjoy yourself.
Travel during the off-season. The weather will be worse, but places will be less crowded and accommodation and airfare will be cheaper.
Take advantage of your hostel's free breakfast, even if it's a little gross and gets old after a while.
Make eyes at the cashier in the grocery store. You never know when he will decide to throw in a free banana.
If you use the tube in London, get an Oyster card. It will save you money every time you use it. Look for similar offers in other large cities.
If you're not in a hurry, walk. If you must take public transport, choose a bus over a taxi (get the idea?).
Check to see if your bank charges a fee for foreign transactions. If it does, consider getting a lot of cash out of the ATM at the beginning of your trip so you don't have to do it often (just don't keep it all in one place, please). Even if it's convenient to just pay with your card all the time, you don't want to come home and find out that your bank was charging you a foreign currency conversion fee for every single transaction.
Amen to what Hermia said about not eating out as a way to save money. Although... I tend to eat out with the money that I haven't spent on souvenirs because food is just such a great way to get a feel for the place that you're visiting. But don't waste your money on... Subway or the like. Eat something cool that you wouldn't find easily at home. It can still be pretty cheap. And if you do opt for the grocery store only route, at least buy things there that you wouldn't buy at home.
Buy produce at an outdoor market rather than the grocery store.
Lastly, I tend to make a hobby out of planning cheap European vacations for myself, so if you have specific places that you are planning to travel to, I may know more depending on whether or not I've ever looked into them. And there are probably things I've forgotten. I'm pretty sure you and I are Gchat friends already if you care for more.
I apologize for not including any links in this. I was lazy. Use Google.