According to the endosymbiont theory, mitochondria and chloroplasts originated as bacteria which were engulfed by larger cells. How many times is it estimated that this occurred in the past? Are there any examples of this process being observed directly?
Well, it seems quite obvious that it was not a single I-eat-you-but-you-survived act but rather a convergence of endosymbiotic and host species into a greater and greater cooperation. Of course this leaves a question if there was one or more species of endosymbionts involved.
Mitochondria are a very primeval story forced by the oxygen catastrophe, so it is hard to say, although great majority of mitochondria seems to have a single origin.
Plastids are much more divergent, however it seems that they did originated from a single source, diverged into chloroplasts, cyanelles and rhodoplasts and were later mixed up by numerous acts of secondary and even tertiary endosymbiosis (plus a further evolution); this variety can be especially seen within Euglenas, and they are the main group investigated in this manner.
I think @mbq has covered the frequency question better than I can.
There is at least one modern example of this kind of new organelle formation. Aphids have a deep, intracellular endosymbiont Buchnera involving some genome transfer that has developed in the last 200 million years.
There are many articles about this topic (eg: Nature from 2000), and it was a little controversial 15 years ago. Now, it's largely accepted that this is a modern development of endosymbiosis, and a confirmation of the theory.
It depends of what you call endosymbiosis. In the sense of mutualistic interaction between host cell and intracellular organism, it also include Rhizobium bacteria and Fabaceae plants, some Cnidaria and algea in their cells, and even some micorrhizal fungi that invade into plants cells. But parasitic interactions are also sometimes call symbiosis, as symbiosis means just “living together” and the balance between profits and costs for each partner are sometimes difficult to measure and even changes in time. So in this wider meaning even Trichinella worm that live in mammal cell is an endosymbiont and endosymbiosis is very common.
There are evidences of secondary endosymbiosis i.e. organelle within an organelle. This is quite evident in Chromaveolates. Many unicellular Chromaveolates which had been classically referred to as unicellular Algae, have chloroplasts derived from other algae. This organelle in turn has a membrane bound suborganelle. For a quick reference you may see this article. Euglena and diatoms are some famous examples of this phenomenon.