What things would a Hindu be willing to die for? Are there any examples of martyrdom occurring in Scriptures, or any reasons a Hindu would be willing to die?
In the Hindu context, a khastriya fights (Although, there have been exceptions too).
To answer the title question:
What would a Hindu be willing to die for?
If we look at the Hindu leaders, just a few centuries back, or look at our soldiers, we see a great spirit of sacrifice for the nation.
You can read about Maharana Pratap, who is venered for his courage even though he lost in the Battle for Haldighati.
This famous poem enunciates the Shaurya of Jhansi Ki Rani who faught valianty against the British and died.
Chhatrapati Shivaji Maharaj, was a Hindu leader most famous for his courage and spirit of sacrifice. He fought under the guidance of his Guru Samartha Ramdas (composer of the Advaitin Vedanta text Dasbodh).
These are only a few examples. There are so many more that can be given.