Screen-Space Ambient Occlusion (SSAO) is quite popular in the moment. ShaderX7 had several articles and there are lots of approaches to gradually improve the effect.
A good way to look at SSAO or any similar approach is to consider it part of a whole pipeline of effects that can share resources and extend the idea to include one diffuse (and specular) indirect bounce of light by re-using resources.
The overall issues with SSAO are:
1. quite expensive for the image quality improvement. Using the astonishing high amount of frame-time for other effects is an intriguing idea. In other words the performance / quality-improvement ratio is not very good compared to e.g. PostFX where a bunch of effects consumes a similar amount of time.
2. a typical problem is that lighting is ignored by SSAO. Using the classical SSAO implementation under varying illumination introduces objectionable artifacts because the ambient term is darkened equally (obviously you can apply SSAO to the diffuse and specular term like a shadow term ... but then it isn't ambient anymore). If you have a "global ambient" light term like skylights, SSAO will diminish the effect. It also leads to problems with dynamic shadows.
Overall I believe a fundamental shift to more generic method is necessary to solve those issues. This is one of the things I am looking into ... so expect an update at some point in the future.