I have limited experience with SPECT and PET, but I can tell you that for CT it is very common to use filtered back projection due to its computational efficiency. Though there is a lot of research investigating the advantages of iterative reconstruction, as well as many developments that greatly increase the speed of these iterative algorithms.

I work in clinical nuclear medicine. Modern SPECT and PET equipment use both 3D ordered subsets expectation maximization (OSEM) for image reconstruction. The resulting image quality obtained with OSEM is generally better than with FBP, with lower noise and no streak artifacts. Additionally one can introduce scatter and attenuation correction routines as steps within the reconstruction process. 

I reviewed the most of range image reconstruction algorithms in the following publication:

Conference Paper A REVIEW OF RECENT RANGE IMAGE RECONSTRUCTION ALGORITHMS

I think that something that needs to be addressed is which one is the worst and by which criteria. If you go to any medical imaging conference it is likely to see new image reconstruction algorithms. These algorithms produce great images in terms of quality but you don't see them being used in the industry from companies that design PET or SPECT scanners.