The United States has long had a tradition of accepting refugees from all over the world. Many Western governments have shown this compassion by allowing refugees into their countries as well. Yes, there are major security concerns regarding Syrian refugees. However, the United States and other Western governments should not ban Syrian refugees from entering their countries. Instead, governments should work together to better vet refugees; ensuring that terrorists are not admitted into their countries.
We can't support all of them, and they need to be vetted as best we can, but we should help if we can. We live in a global society and we would want the same help if we needed it. Our allies should also help, so if everyone pitches in, it's a shared burden and hopefully we can work to make it temporary and safer for those who would like to go home again.
A country should not have to be forced to take in refugees from another country and nor should they be frowned upon for not doing so. It is that country's responsibility to do what is best for their country and if they think it good to take in refugees then good for them but if they feel it would do harm to their country to bring in refugees then they have the right to turn them away.
Countless examples already exist of the vetting process not being enough to even catch the most obvious of potential terrorists.
Not only that, there is currently no standard way to determine where exactly these refugees come from or believe in.
The second of these two is the most important. It should be determined to what extent they believe in the principles of Islam and which principles those are. Once that is determined there should be a threshold, or certain principles, that are not acceptable.
Examples such as the belief that apostates should be killed, honor killings are acceptable, rape of women is acceptable, etc. These are all principles in the holy texts of Islam and are completely incompatible with western values and constitutional rights.
Furthermore there should be very cautious placing of refugees. Do not place them all in one area but attempt to spread them to tolerant areas where assimilation would not be difficult (relatively speaking).
Any refugee who commits a crime should be deported and black-listed from ever traveling here again.
First, the U.S. is not responsible for bringing turmoil to the region - it has existed there since the beginning of time and is likely to continue. Secondly, Syria has never been a U.S. ally and has traditionally sided with the Soviet Union and Russia in disputes throughout the 20th century. Western governments do not have the ability to properly investigate these people and their primary obligation is the protection of their citizens, not the accommodation of refugees who really do not want to resettle here in the first place and have no desire to assimilate into our cultures.