Most hostels in cities have better outside security than hotels that are quite a bit more expensive. Not all hostels have that though, so use your brains and ask if in doubt.
Pack your belongings in your pack when you do not use them and use the locker hostels always have. Keep your important/expensive items with you all the time (or behind safe locks.)
Try not to chose hostels where you are about the only guest. Likely not dangerous but it may feel that way when you are the only person in a big dorm.
They are safe, to a certain extent. Don't let others at the hostel know what you are traveling with and never discuss your finances with them. Lock up your passport, wallet, purse, phone, camera, medications, etc in the locker. Withdraw only as much cash as you need from the ATM, and when you are going out go only with as much cash as you think you might need for the day. When you travel and stay in a hostel, don't bring expensive clothes or anything that costs a lot of money. Someone who sees you with these things will try to steal them. Keep your cash deep down in your front pants pockets..not in a wallet and not in your back pockets. Pickpockets are notoriously rampant throughout Europe.
You can always find beforehand hostels in the cities you will visit that can have good reviews and comments. Apart from that, keeping your wits and exercise common sense you will have no problem. Pickpocketing is indeed a great problem in any country and for that you will have to extremely careful.
Hostels are usually frequented by people of your age and they too will have similar concerns and they will also be wary. On this, big numbers offer safety. Find someone that will suit you and spend time together, watcging out for each other.
Hostels in Western Europe are safe, it's only in some Eastern countries (You've seen Hostel? Those ones) that you really need to be careful.
I have been staying in hostels since I was 18 years old and have never had any problem. Just don't ever leave any valuables unattended in the room, even when you go to breakfast or to take a shower. At a hostel in Amsterdam while we were at breakfast someone had come into the room and stolen things out of people's backpacks. Luckily my friend and I had our daypacks with us with our cameras, passports, etc. But another girl staying in the room had her wallet, passport and phone stolen out of her bag
But in terms of physical safety you will be fine. I have never seen or heard of any violence happening in a hostel
Hostels in Europe can be safe and even cozy -- or they can be seedy and scary, depending on the one you choose. Although hostel theft and personal safety are generally not major problems throughout Europe, you can end up in a grimy hostel that lacks basic amenities, such as a flushing toilet. Using common sense and researching a hostel through a directory, fellow travelers or in person helps ensure your safety.
Hostels are nice and they have lockers etc. Also check: couchsurfing.com (very nice) and also you might like housesitting.com. Never carry too much cash (use debit credit cards). Never carry a purse. Safer that way.
There's very little physical violence in Europe. There is, however, a lot of pickpocketing. You have to be very careful with your possessions in a hostel.
