These are the listing of thousand names of each God. If you go through them critically you may not find that all these thousand names are different and we find that several names are repeated. The most famous of the Sahasranamams are the Vishnu sahasranamam and the Lalitha Sahasranamam. Shiva Sahasranamam and Lakshmi Sahasranams are also relatively popular.Saharanamams are available for most of the incarnations of Lord Vishnu and all other Gods and Goddesses. Trisathi giving 300 names, ashtotharams giving 108 names, Satha Nama stotrams giving one hundred names , Shodasa nama stotram giving sixteen names and Dwadasa nama storams(12 names) also belong to this category of stotras.
These are possibly the most popular form of Hindu stotras. These normally contain eight verses praising the God or Goddess. Most of them are very simple and easy to understand. There is a phala Sruthi attached to every ashtakam giving the possible effect of chanting that particular prayer.
These are another very popular form of prayers addressed to Gods as well as planets . Essentially they request God to protect different parts of our body as well as mind. It also requests God to protect us in different circumstances. Narayana Kavacham is one of the most famous in this category.
These are similar to ashtakam but with ten Stanzas.
These are prayers with five stanzas.
These are again similar to ashtakam but with six stanzas
These are prayers with seven stanzas.
These are longer prayers with fifty stanzas
These are still longer poems with five hundred stanzas.
These are supposed to be the king of prayers addressed to a particular God. Though they are not available for all Gods, many of them are available.
These as well as Bhujanga prayatha stotrams are supposed to move like a snake. Adhi Sankara is credited with composing many such Bhujangams. His “Subramanya Bhujangam” is very famous
These are stotras where there is no restriction on the length of a line of a stanza. Some of the Dandakams are very long prayers with just one line. Shyamala Dandakam of poet Kalidasa is the greatest in this category.
These prayers are addressed to the God requesting him to extend his hand in support to us. The Lakshmi Narasimha Karavalamba stotram of Adhi Sankara is possibly the most famous.
These are prayers addressed to the lord to wake him up. The oldest among this type of stotras are the thirupalliyezhuchi in Tamil and the most famous is the Venkateswara Suprabatham.
Lahari means waves. In this form of prayer the stanzas follow each other like waves. Soundarya Lahari of Adhi Sankara is possibly the most famous.
These are tamil prayers written by the great Vaishnavite saints of Tamil Nadu called the Azhvars.
These are again Tamil prayers written by Nayanmars , the Tamil saints eulogizing Lord Shiva.
These are Hindi prayers praising a particular God. These are available addressed to almost all Gods.
These are again Hindi prayers but have forty stanzas each. The most famous is Hanuman Chalisa composed by saint Tulsidas.
Gadhyam means prose . Some of the Vaishnavite saints wrote prayers in prose and the most famous is the Gadhya Thrayam written by Saint Ramanuja
These are prayers written in Marathi by those great devotees of Pandharpur,
Mangalam means auspiciousness and these are prayers which are sung at the end of chanting of prayer sessions as the last prayer.