Sri Ranganatha Ramayanam – Gona Budhha Reddy
Gona Budhha reddy of 11th century had written Ranganatha Ramayanam in telugu, with few changes in the incidents which effected the course of the events.This was written in DWIPADA metre which shows the authors mastery over the poetic art. His son Gona Ganna Reddy was an independent King in the Kakatiya Empire.
Molla Ramayanam - Molla
Atukuri Molla a contemporary of Srinatha kavi and one among the first few female Telugu poets. Her work is known as Molla Ramayana and is still one of the simplest of many Ramayans written in Telugu. With the first poem it self she says that "Ramayana had been written many times. Does someone stop taking food because it has been taken every day? So is the story of Rama and one can write, read and love it as many number of times as possible."
Bhaskara Ramayanam - Bhaskara
Bhaskara Ramayanam is one of the Classics of Telugu language with its grandeur,cartistic perfection and literary excellence..cHulukki Bhaskara along with his son Mallikarjuna Bhattu, his student Rudradeva had initiated to write Bhaskara Ramayanam, but could not complete it, Ayyalarya completed it later.
Champu Ramayanam – Bhoja Raja
Champu Ramayana, a re-narration of the Ramayana in mixture of prose and poetry, which characterises the champus. The description of Hanumat’s qualities are particularly poetic. Written by Bhoja Raja a Rajput king who ruled Malwa region in 11th century.cChampu is a genre of Indian Literature of Sanskrit language which consists of both prose and poetry.
Ram Charith Manas - Tulasidas
Ramacharitha Manas is regarded as "the greatest book of all devotional literature written by Tulasidas of 15 century. Tulsidas claims to have received the story through his guru, Narharidas. Tulsidas was unconscious and the story was stored in his mind (Mānasa) for long before he wrote it down as Ramacharitha Manas.
Kamba Ramayanam - Kamban
Kamba Ramayanam of Kamban is an epic of about 11,000 stanzas, as opposed to Valmiki's 24000 couplets. Kamban or Kambar of 12th century is praised by many Tamil poets, statesmen, kings, and common people for his Kambaramayanam.
P.S. There are many regional versions of Ramyanam, only few of which are rich in literature and gained the appraisal of common people to a large extent are mentioned here. There are also many versions of Ramayana outside India also.