Here is the list of all the recognized national parties and their reserved party symbols. In addition to this there are many political parties that are recognized at the state level.
Also there are parties who are registered but yet to be recognized by the election commission of India.
National Parties and their reserved Symbols
1.Bahujan Samaj Party BSP - Elephant
[ In all States/U.T.s except in the States of Assam and Sikkim, where its candidates will have to choose a symbol from out of the list of free symbols specified by the Commission ]
2.Bharatiya Janata Party BJP - Lotus
3.Communist Party of India CPI - Ears of Corn and Sickle
4.Communist Party of India (Marxist) CPI(M) - Hammer, Sickle and Star
5.Indian National Congress INC - Hand
6. Nationalist Congress Party NCP - Clock
7. Rashtriya Janata Dal RJD - Hurricane Lamp
For more details you can check this notification regarding Party Symbols, released by Election commission of India: