gravity - How does light affect the universe?

Old question, but I'll address something that hasn't been brought up by the previous answers.

Photons $simeq$ CMB photons (to first order)

As the others has already said: yes, light has energy and hence it gravitates. The bulk of photons that permeate the Universe isn't of stellar origin, though, but is in fact the cosmic microwave background, the energy density of which several orders of magnitude larger than other photons, as seen in the graph from this answer to "Number density of CMB photons". In terms of number density, there are 4-500 photons per cm$^3$.

Space is big and isotropic

Since CMB photons are isotropically distributed, the ever-so-small radiation pressure is equal in all directions, and hence cancels out. And although we're all the time bombarded by both CMB photons and stellar photons, space is so mind-bogglingly big (D. Adams, 1978) that if you consider a random photon in the Universe, the probability of it hitting anything at all is negligible. Roughly 90% of the CMB photons have traveled for 13.8 billion years without hitting anything; the remaining 10% interacted with the free electrons that were released after reionization, but weren't absorbed, just polarized, and by far most of these interactions took place shortly after reionization; by now, the Universe has simply expanded too much.

Photons are redshifted

Although there is energy in photons, and hence they add to gravitation, first of all they're homogeneously distributed in the Universe (and thus pulls equally in all directions), and second their energy density is negligible compared to baryons ("normal matter" like gas, stars, and planets), dark matter, and dark energy. In fact, their relative densities are ${rho_mathrm{bar},rho_mathrm{DM},rho_mathrm{DE},rho_mathrm{phot}}/rho_mathrm{total} = {0.05,0.27,0.68,10^{-4}}$. But this was not always the case. As the Universe expands and new space is created, the density of matter decreases as $1/a^3$, where $a$ is the scale factor ("size") of the Universe. The same is true for photons, but since additionally they're redshifted proportionally to $a$, their energy density decreases as $1/a^4$. That means that as you go back in time, the relative contribution of photons to the energy budget increases, and in fact until the Universe was 47,000 years old, its dynamics was dominated by radiation.