Cumin is used frequently whole and in spice mixes to add a characteristic smoky note to Indian dishes.
Turmeric is another common Indian spice. Grown as a rhizome, it can be used fresh (like ginger) or dried.
Coriander is probably the most ubiquitous of spices in the Indian spice rack.
Asafoetida or hing is used during the cooking process or tempered in oil as the first step before adding other ingredients. It is a flavouring agent.
Kashmiri chillies, milder in heat it adds a vibrant red colour to the dishes as opposed to just heat. Unique to Indian cuisine it sure is a must try chilli powder.