I feel very comfortable saying that, in general, kidnappings in Yemen are a thing of the past. There are still areas that are closed off to tourists, and some areas that are of higher risk that others. But, in general, Yemen feels like a very safe place to visit.
Six months prior to my visit was an Al Qaeda attack at the tourist site in Marib that killed several tourists from Spain. Though this was still a hot topic on the minds of the people I spoke to, they all say it as a shameful act and hoped that tourists would realize Yemen is not a dangerous place. I likened it to the image the Bronx has. When people here the name "Bronx," they automatically think it means it is a bad place. But, I live there and have never had any problems.
Before my visit, I had also read that tour groups travel in convoys and are guarded with armed guards and vehicles. Not once did I have a guard with me, nor travel in a convoy, nor have an armed vehicle escort me. To me, if I did travel with armed guards, it would only draw attention. I traveled throughout Yemen in a 4x4 vehicle, with just a driver and guide (sometimes just a driver). There were several police checkpoints we had to pass through, but none of them gave us any problems when we told them I was an American (or Canadian in some places).
One image of Yemen that was burned into my mind before going was that everyone carried a gun. This is not true anymore. Recent laws passed within the country forbid people to bear arms in public (I believe it was enacted so tourists would be less scared). So, on my arrival I was quite shocked to see no one carrying a gun. I think throughout my trip I saw less than five men carrying guns.
So, in short, Yemen is a safe place to visit. Not once did I feel threatened or that I was in any danger. Tour companies take the necessary precautions to make sure you have a safe and pleasant trip. And, even without a tour company, the people of Yemen put you at-ease and make you feel welcome.