Related deities and entities associated with Apollo
Helios was the titan equivalent of Apollo, being in the hellenic mythology as well… He is a titan that is associated with the sun.
The roman counterpart of Apollo also is Apollo but the personality changes from one place to the other. I think the roman ones are more war-like gods. The roman titan equivalent would be Sol.
If we were seeing in the egyptian mythology the “equivalent” would be Ra, god of the sun. Or even Khepera (Khepri) and/or Khnum, because those are seen as aspects of Ra, the sun. It may also be Sekhmet, she is associated with healing and causing plagues as Apollo, she is seen as the most hot sun, the sun of the midday. Or even Atum, Amun or Aten (you see, egyptian mythology had many associations and deities that were syncretic, and this way both the deities were seen on that aspect). Heru (Horus) is also associated with Apollo.
In the norse mythology I guess would be Sól, Baldur or Freyr.
In the celtic myhtology would be Belenus (in the wikipedia it says that he would be very like Apollo) or Alaunus (who also has to do with prophecy and healing). It could also be Lugh (being associated with arts and crafts), or Brigid (associated with healing, sometimes sun and poetry).
In the caannite mythology would be Shapash.
Surya is a solar deity and could be associated with Apollo, in the Buddhism, Hinduism or even Jainism.
Amaterasu is the solar deity in the japanese mythology and in the Shintoism.
As I am portuguese, I’d love to add the lusitanian mythology, and here the solar deity would be Endovelicus (he would be very much like Apollo, also having oracular functions and associated with healing).
The Maya sun god is Kinich Ahau (aka Ah Kin).
If you are interested in learning about more solar deities, click here.