Why can't "missing mass" (=dark matter) be photons? After a star lives and dies, I assume virtually all of its mass would be photons. If enough stars have already lived and died, couldn’t there be enough photon energy out there to account for all the "missing mass" (=dark matter) in the universe?
And if there were enough photons to account for all the missing mass, what would it look like to us?
 A: Photons are easily detectable. We can count how many photons are there at any distance of us by just counting the photons reaching us from there. It is impossible that the hidden photons ramble the whole universe but mysteriously avoid us.
A: As a general rule, zero mass particles which travel with the velocity of light are not good for dark matter, because dark matter concentrates around gravitational attractors. It has to be particles with some mass that can be at rest in order to stay around a galactic center from the beginning. In addition they have to be controlled by weak interactions, if they decay, because the dark matter halo is stable for long periods.
Maybe I should add that very cool photons from the beginning of the formation of the observed universe exist and have been detected as Comsmic Microwave Background radiation, very low frequency photons, uniformly distributed in the cosmos.
A: I just want to point out that it seems some people may be conflating 'dark matter' with 'dark energy.' Regular "normal" matter like electrons, neutrons, and the like, are estimated to make up about 5% of the matter/energy density of our universe.
Dark matter, estimated to make up about 25% of the matter/energy density of the universe, is matter that has mass, but the gravitational  and other effects of which are not directly visible. Dark matter is somewhat mysterious but could easily be something like exotic particles or oceans of black holes between galaxies. 
Dark energy, is the real mystery; it makes up the other (about) 70% of the matter/energy density of the universe needed to explain inflationary cosmology and expansion/acceleration of the universe.
Photons are mass-less particles that embody energy, visible when they strike objects. I think it's an interesting notion that the energy from photons could at least in part constitute some of solution to the "missing" dark energy problem. As has been pointed out, it's difficult to reconcile how so much of the "missing" energy could have come from so little: the 5% ordinary matter creating all that dark energy. But I don't see anything impossible about this idea generally. Perhaps the dark matter also contributes to this somehow. There may even be dark-electromagnetic forces that create dark-photons, this may be seen as extra-dimensional as one poster referenced earlier. 
"It’s humbling to think that ordinary matter, including all of the elementary particles we’ve ever detected in laboratory experiments, only makes up about 5% of the energy density of the universe." _Sean Carroll
With so little of what we are used to seeing and interacting with in ordinary meaningful way actually making up what exists, speculation of what else is out there is not only justified but necessary.
A: There is a simple argument why photons emitted by stars can't be dark matter, and that's because there is about ten times more dark matter than normal matter. If all the stars created at the Big Bang had turned into photons there still wouldn't be enough of them.
You might argue that maybe more normal matter than we think was created during the Big Bang, but the theory of Big Bang Nucleosynthesis places a limit on how much normal matter was created, and this limit is four times smaller than the amount of dark matter. The dark matter has to be something odd.
If you're interested in more info this paper is a good review, though harder going than the answers here!
A: Photons don't have mass. So your assumption's incorrect, although I don't know how much of a (say) main sequence star's mass gets converted into photons over its lifespan. 
Photon's can't account for, say, dark matter, because dark matter has mass.
Thermal energy (in the vacuum) is comprised of photons, which can spontaneously form particle-antiparticle pairs. Usually these quickly annihilate, so this is also not a good source of mass.
A: It is accepted that the early state of the universe was mainly radiation, then we had expansion; radiation cooled down as a result, and condensed into matter. The pressure of a photon/radiation gas is positive and given by an equation that resembles the universal gas law; PV=.9 NkT (https://en.wikipedia.org/wiki/Photon_gas). 
So by logic, the total(equivalent) mass or the total condensed energy in the universe, must be less than the total radiation at the start. If also the condensation process involved only a small portion of that radiation, then surely we should have plenty of radiation left uncondensed- and could easily be much more than that of all matter. This remaining gas is continuing its expansion of course- today and in the future.Since momentum levels follow energy levels for photons, there must be plenty of momentum around too- due to radiation that is exerting pressure on the various matter objects, producing some expected and may be not so expected situations. If we accept this point of view, one can do detail calculations to get the full picture. The rate of expansion could be one useful result to compare with present data.
