Actually the first "real" Nuclear Fusion reactor is being constructed as the ITER project.
Although they started digging in France, they are many problems yet to overcome. I put real into quotes because the goal of a reactor is to produce more energy then what is used to start the reaction, and this is one of the things that nobody has been able to achieve yet with fusion, as mentioned here.
Sorry for this introduction but it felt necessary. Now, for the dangers, a list is compiled here and the process seems really safe since in case of a problem, everything stop in a few seconds.
Of course, they are, as mentioned, many obstacles yet to overcome, and if the theory makes it safe, the implementation will create other variables.
Therefore, since we don't have a working prototype yet, we don't really know. Maybe on physics stackexchange you could have a more thorough answers.
I was to lazy to check, but @dmckee posted in the comments this link to physics.SE where they have this discussion! They say basically the same thing ;).