There were nine grammars for Sanskrit available in ancient days. They are –
ऐन्द्रं चान्द्रं काशकृत्स्नं कौमारं शाकटायनम्।
सारस्वतं चापिशलं शाकलं पाणिनीयकम्॥
Source of this Shloka is not known. However, there are references that this verse is from श्रीतत्त्वनिधि – a Vaishnavite treatise. I could not get this verse any where. Aindram, Caandram, Kaashakritsnam, Kaumaaram, ShaakaTaayanam, Saarasvatam, Apishalam, Shaakalam and PaaNiniiyakam. These are named after their authors. They were authored by Indra, Candra, Kaasjakritsna, Kumaara, ShaakaTaayana, Sarasvati, Apishali, Shakala and Panini. Here Kaumaara is also known as Kaalaapam and Kaatantram according to some scholars. Kaumaaram is available partially in Garuda Purana and Agni Purana. ShakaTaayana is also available partly which has been published and UNaadi Suutraas – a special category of grammar aphorisms in 10 chapters authored by ShaakaTaayana is completely available now and published. Saarasvata VyaakaraNam is also available and published. Apishali VyaakaraNam is aprtly available. Shaakala Vyakaranam is available as quotes in various VyaakaraNa texts. PaaNiniiya VyakaraNam is available in full and is in teaching-learning tradition now all over the world.
There is another version that there are only Eight Grammars only. There are various versions of these eight vyaakaraNas. Let me quote one such version. Bopadeva in his work Kavikalpadruma mentions the following eight grammars –
इन्द्रश्चन्द्रः काशकृत्स्नापिशली शाकटायनः।
The verse सोऽयं नवव्याकरणार्थवेत्ता ब्रह्मा भविष्यत्यपि ते प्रसादात् ॥ is in 36th chapter of Uttarakanda of Ramayana. However, this verse has no commentaries of any commentators. Further, in all editions this verse is not found. Hence, it is inferred that this is an interpolation. Whatever, it may it is in praise of Hanuman.