We all know that Lord Krishna didn't marry his lover Radha, but we still consider her as the consort of Lord Krishna. My question is why do we worship them together?
Besides the Brahma Vaivarta Purana mentioned in the other answer, the 39th Chapter of the 9th Book of Devi Bhagavatam also mentions the origin of both Radha and Lakshmi from Krishna:
4-33. Nârâyana said :-- Of old, in the beginning of the Prâkritik Creation, from the left side of Krisna, the Supreme Spirit, appeared in the Râsamandalam (the Figure Dance) a Devî. She looked exceedingly handsome, of a dark blue colour, of spacious hips, of thin waist, and with high breast, looking twelve years old, of steady youth, of a colour of white Champaka flower and very lovely. The beauty of Her face throws under shade millions and millions of autumnal full moons. Before Her wide expanded eyes, the midday lotus of the autumnal season becomes highly ashamed.
By the Will of God, this Devî suddenly divided Herself into two parts. The two looked equal in every respect; whether in beauty, qualities, age, loveliness, colour, body, spirit, dress, ornaments, smile, glance, love, or humanity, they were perfectly equal. Now she who appeared from the right side is named Râdhâ and she who came from the left side is named Mahâ Laksmî. Râdhâ wanted first the two armed S’rî Krisna, Who was Higher than the highest; then Mahâ Laksmî wanted Him. Râdhâ came out of the right side and wanted first Krisna; so Krisna, too, divided himself at once into two parts. From His right side came out the two-armed and from his left side came out the four-armed. The two-armed person first made over to Mahâ Laksmî the four armed One; then the two armed Person Himself took Râdhâ. Laksmî looks on the whole universe with a cooling eye; hence She is named Laksmî and as She is great, She is called Mahâ Laksmî. And for that reason the Lord of Râdhâ is two-armed and the Lord of Laksmî is four-armed. Râdhâ is pure Aprâ kritic S’uddha Sattva (of the nature of pure Sattva Guna, the illuminating attribute) and surrounded by the Gopas and Gopîs. The four-armed Purusa, on the other hand, took Laksmî (Padmâ) to Vaikuntha. The two-armed person is Krisna; and the four-armed is Nârâyana. They are equal in all respects.
Therefore, Radha & Lakshmi are on the same level and hence she is worshiped along with Krishna just as Lakshmi is worshiped with Lord Vishnu & her incarnation Sita is worshiped with Shri Rama.
Because She is indeed half body of Shri Krishna in the following way:
आबिर्बभुव कन्यैका कृष्ण्स्य वामपार्श्वतः
धवित्वा पुष्पमानिय द्दातर्ध्य प्रभो पदे
रासे सम्भुय गोलोके सा दधाव हरे पुरः
तेन रधा समाख्याता पुराविद्भिद्विजोतम [BVP - 5.25,26]
Then a maiden manifested from the left portion of Shir Krishna. She ran and obtained flowers to offer onto the feet of Shri Krishna. O best of the priests, because she originated from the rasa(ra) in Goloka and dhavitva (dha), i.e. ran in front of Hari, scholars call Her Radha.
So in Goloka, the abode of Krishna, it is Radha who is the consort of Shri Krishna. It is Shri Radha who becomes Lakshmi, the consort of Vishnu, in Vaikuntha, Sita, the consort of Rama, in Treta yuga and Rukmini in Dwapara. We generally worship the Lord along with His consort as the Shakti-Shaktimaan duo. So Radha being the consort of Krishna, they are worshiped together.
If you are interested to know whether they were married or not, and if not then why, then you can refer to this answer.
A brief answer, source linked at the end.
- The love between Radha and Krishna is not a mundane love like in this material world. Therefore, we can't apply normal moralistic standards here.
- Another story in the Brahma Vaivarta Purana states that they were indeed married by Lord Brahma
- On a more esoteric level, Radha is married to Abhimanyu, who is but an expansion of Krsna. However, for the purpose of rasa, or spiritual mellow, Radha and Krishna are in the mood of separated lovers, which makes Their spiritual love more intense.
Krishna is the supreme God, only for the followers of Gita and Bhagwatam. Krishna, as a God, is a creation of the puranas and Gita. Vedas have nothing to do with this Krishna that has been raised to the Supreme God by the Puranas.
Neither any Samhita nor any Brahamanam mentions this Krishna. He is never a Vedic God. It may be pertinent and proper to say that Krishna, the pauranic God,, is a non entity in the vedas. He is no where mentioned in the vedas, none of the traditional commentator has been able to find out Krishna in the vedas. Even where the very word “Krishna” is found in the vedas, the same has been explained as the herbal plants, the black buck, or even a sage. But nowhere it has been used for the God. Even the word “Keshav”, synonymous with Krishna, means an eunuch in the vedic lexicon.
Vedas glorify Indra since Indra is the king of the Gods, the very epitome of courage, force and power, in the vedas. Indra is the foremost God, and has the lion’s share of the vedas dedicated to him. He is the God of the atmosphere, brings rainfall, provides wealth, kills the demons and is feared by all of the evil forces. Indra is the foremost power of nature.
The difference is between the puranas and the vedas. A few of the Puranas state Krishna to be supreme God, while all of the Vedas praise Indra as the best of the Gods. But since vedas are superior to the Puranas, and are to be followed when there is any conflict, Indra prevails. That is why the followers of puranas have coined so many derogatory stories about Indra, only to show him in a bad light. This is also the reason that Krishna based sects do all efforts to show that Krishna is mentioned in the vedas, but they do not find any single of such verse in any of the samhita or brahamanam to prove their point, they try for pervert translations, but the same are caught in the act, since none of these is supported by any of the traditional commentators.