How many times did photosynthesis evolve?

The emergence of photosynthesis has occurred rather independently in multiple organisms. One way of looking at this is to look at the taxonomic distribution of photosynthesis reaction centers, which points to 5-10 origins according to current data (mostly in bacteria). That number has some big error bars as we are talking about very deep, old branches of the tree of life.

There are other criteria that we could use- for example the evolution of carbon fixation. However, that includes also chemoautotrophy, and is thus a bit more expansive.

Note that by some definitions the acquisition of cyanobacteria in plants may not even represent an independent emergence of photosynthesis, as the cyanobacteria already did photosynthesis!

If your question is more narrowly "how many times did photosynthesis evolve in eukaryotes" (not bacteria or archaea), then you would also need to include animals that do photosynthesis in a way similar to (though I believe less efficiently than) plants. They seem to similarly use endocytosis to acquire photosynthetic machinery from photosynthetic cells that they eat.

Update In response to comment from @shigeta, I'll add that the review that I link focuses on the reaction centers (RC) genes. They note that the RC genes probably had a single emergence, but that horizontal gene transfer is probably responsible for the current distribution of the organismal trait of photosynthesis:

Significant evidence indicates that the current distribution of photosynthesis in bacteria is the result of substantial amounts of horizontal gene transfer, which has shuffled the genetic information that codes for various parts of the photosynthetic apparatus, so that no one simple branching diagram can accurately represent the evolution of photosynthesis (Raymond et al., 2002).

Im going to expand my comment into an answer because the discussion was just too interesting.

the conclusion at the bottom of the review cited is: "Current evidence suggests that the earliest photosynthetic organisms were anoxygenic, that all photosynthetic RCs have been derived from a single source, and that antenna systems and carbon fixation pathways have been invented multiple times." you can see on their phylogenetic tree that the RC1 and RC2 appear on all these branches, which implies they came from the same ancestor, lost in time.

@maximillianPress points out in his comment that lateral gene transfer is very common and this creates the exact pattern Many gene functions can arise more than once, but when you look at the gene, if a protein is achieves a function, like RC1 and RC2 their shape and detailed sequence will not resemble each other.

A classic example is the evolution of the eye. Eyespots and photosensors with lenses have evolved many times in microbial evolution and in may have evolved separately in molluscs vs vertebrates depending on how you define it. Light detection is a microbial innovation and the opsin light sensors in animals bear a strong resemblance to those in archaebacteria.

Enzymes form a clearer example. Studies of some of the carbohydrate metabolizing enzymes show that some specific roles are filled by multiple very divergent protein families. The role of a protein may change over time but its very unusual for the way the protein folds to change.

An third example is the crystallins whose function is to form the lens of the eye which has to remain stable for a lifetime. In different animals these genes are radically different - distinctly different proteins can fulfill this role. that is a gene role which may have evolved twice, but the role is fairly broad so its been filled by different proteins in different parts of the evolutionary tree more than once.

My thought is that the lateral transfer of microbial genes may confuse the evolutionary tree but the difficulty of creating a photoreaction center is much higher. There is only one bacterial reaction center protein family, so the predominance of evidence is that this phenomenon only evolved once and may have been transmitted by lateral gene transfer many times since.