Amsterdam is given a bad reputation in this thread. Take it from someone who has lived there for the past 12 years: the city (at least the part that tourists visit) is entirely safe. Plus a lot of good museums, beautiful scenery, lively night scene, loads of music... really worth a visit, but the same is true for the other cities on your list.
I had a couple of bad experiences in Rome. The problem though is that this is really just random bad luck. You might get raped in Venice; you might get mugged in Berlin; you might get drugged in Vienna; you might be ran over as an accidental victim in a hit-n-run in Zuerich. These things happen. But none of the cities, amsterdam included, are unsafe. Come and check for yourself.
@bentivogli: What do you say about my experience in Het IJ? Is the area really that bad? I saw a mosque, which is usually a sign that there are many migrants around, but since it is so close to the city centre (only a short hop with the ferry) I thought it would be more upscale.
Your experience is atypical to say the very least. I know the area just north of IJ very well; although the eastern part of that neighbourhood is poor, and there is not much reason why you should go there (the western part is wealthier, and more interesting architecturally), it is safe. Crime rates are low, esp. violence, and even perceived safety has been on the rise since the past couple years.
I would definetely reconsider and put Amsterdam back on your list. It is a very safe city, I have been there many many times for both work and play and I have never seen any trouble there. It is a beautiful city and unlike anywhere else in the world.
I'm gonna chime in and hope you'll put Amsterdam back on your list. I felt very safe the entire time I was there and didn't run into any problems. Agree with the others that it's beautiful and has lots going for it, and it would be a shame to miss it. I loved the Rijksmuseum and the Bloemenmarkt, and had a great time exploring the city. You can even do day trips to nearby places like Haarlem, it's all very convenient. I believe if you just take the necessary precautions that people generally do when travelling, you'll be perfectly fine in Amsterdam.
[ Edit: Edited on 13-Jun-2009, at 13:23 by summer910 ]
Its been a few years since my last trip to Europe, but I was 20 and did alot of traveling by myself while I was there. The only real problems I had were from overly amorous men. Nothing bad ever happened, but the situation could have turned dicey if I hadn't put my foot down. There were a few incidents where men on trains would bug me and I know it was because I was alone (some men have trouble believing a woman is alone by choice). I found that telling them my husband was waiting for me at the train station was enough to send them away. One did hassle me becuase I didn't have a ring, but most got gone in a hurry. If you use common sense you should be okay. One the other hand, if your looking to meet men; then you should have a pretty successful trip. If you don't want to be approached, just act unapproachable. Also, pretneding not to speak english or whatever language they speak is pretty good to. As for actual crime, I never had any problems just using common sense and taking basic procautions. Hope this is some help. I am getting ready for another trip by myself, so I understand your concerns.
Out of that list, I would say Rome is the least safe but it is also the most fascinating city out of that list, especially if you really wish to see ancient and modern together. It's really thought-provoking and I'd still go and just avoid the Spanish Steps and Terminal train station after dark, i.e. common sense.
You could easily do in 10 days Vienna-Venice-Rome without it costing too much but Italy's accommodation in likes of hostels is really not that great. There's only one IYHA place in Rome for example so it obviously books up fast, ditto Venice. So whatever you do, definitely book in advance!!