Is travelling to the West Bank safe?

I'm currently living in Bethlehem in West Bank (for three months), I'm Spanish.

It is safe if you are tourist and don't go to demonstrations or activist events.

Israeli security forces will make you a lot of questions in the Ben Gurion airport (or in the airport in your country) about your visit for "security reasons" and maybe some will be private (of course you can answer or not). They will tell you (maybe) that Palestinian are terrorist and to travel along West Bank.

This is not true of course but if you stay in Israeli hotels is better for them. I've spent two months and a half here and I feel as safe as in Spain with exceptions as someone told you. Nablus, Hebron, Tulkarem are places with more tension. Also you can find places with clashes between the army and youth Palestinian in Bethlehem (Al-Khader village), Ramallah, Jerusalem (East Jerusalem, Issawiya), etc... but not in the touristic places.

About the situation in Syria of course is not the best, but with the internal conflict they have enough. Syria can't fight against Israel and rebels forces at the same time.

The security situation in this region is a bit precarious, but that's nothing new. It has always been so.

This means that you can go there, but that you have to be cautious. The Syrian crisis is not a reason to stop traveling to Israel. The same if true for the West Bank. Indeed, there are some more dangerous places in the West Bank, especially in the North. The situation in Hebron is also tense. However, Bethlehem, Ramallah, Jericho and the Dead Sea area are okay. If you stay on the "beaten track" there should be no problem.

A region in Israel that is perhaps a bit more exposed are the Golan Heights. This area has a border with Syria. Occasionally, some mortar shells from Syria land there. Not later than yesterday (15-05-2013), shells have landed near Mount Hermon, a recreational area. So, there might be restrictions to travel over there. If there is danger IDF is closing the area partially or totally.

My advice is to closely monitor the situation over there, especially in the West Bank and in the Golan Heights. Follow some news sources, and also the travel advice offered by the different Ministries of Foreign Affairs. It is always worthwhile to check more than one of these sites. The appreciation of a situation can differ. Not everybody evaluates a situation in the same way. For the West Bank, or the particular places you want to visit there, I would set a "Google Alert" or something similar. This allows you to follow the situation on a daily basis.

The following question may also be relevant for your purpose:

It is safe to travel in Israel and Palestine?

I've been there a few years ago so I don't really know how recent facts affected the safety of that area but since it has always been a "conflict zone" I'll give you my two cents.

Jerusalem isn't considered to be in the West Bank. Fully equipped Israeli soldiers are deployed everywhere in the city as are security cameras. It's a very sensitive area but I've never felt in danger, mostly because I was overwhelmed by the beauty of the city itself, I guess. Except the 2011 bus stop bombing, there were only minor terrorist attack in the city in the recent years most of them involving people on truck running over cars and other people. I felt very safe walking around the city at anytime, especially in the old city area. Petty crime rate is very low. Terrorism is a threat, as it is in many other countries nowdays, but they have very good measure against it and you will found this out yourself as soon as you land in Israel. Depending on your religious belif (and how much you show it off) you may be target of hate crimes which is still rare in touristy areas.

Bethlehem and Ramallah are actually inside the West Bank but keep in mind that the Israeli army can come and go almost as they please. In fact, there are multiple checkpoints inside the West Bank and you will be surely stopped by many of them on your route to Bethlehem/Ramallah. While this doesn't mean it's perfectly safe I felt okay there except when I was travelling with an American I met in Jerusalem (I'm Italian) and I remember that when we arrived in Bethlehem, on our way to the Church of Nativity, we have been stopped by a group of Palestinian that started harassing my American mate asking him if he actually was American. They totally ignored me, probably they soon understood by my accent that I wasn't American, and he managed to get out of that situation too since he is originating from Costa Rica and played this card quite well. So if you are from the USA I wouldn't go around whistling "Star Spangled Banner".

One suggestion I think you should keep in mind while travelling in these sensitive areas is to keep a low profile. Never get in an argument about politics or religion or other sensitive topic with people you don't know very very well. I found many Palestinian (taxi driver mostly) complaining with me about their situation. Whether you empathize with them or not try to remain neutral.