Characters being hurt emotionally is extremely important. It is a part of every genre, as the physical side is not. Our beloved fictional people become so loved by us because of this emotional hurt. In the Ilyon Chronicles by Jaye L. Knight, most of the readers have fallen in love with Jace because of his past and his personality. (I won't spoil what his past is for you. You will just have to read the book :D) We just can't help wanting to give him a big hug!
So how can you hurt your characters emotionally? There are many ways to do it (so many that I cannot name them all here)! It also depends on the genre. It would be a little weird if the MC's best friend was murdered by an alien in a contemporary novel.
1. Someone close to your MC dies.
The way they die will most likely vary according to your genre. How will this affect the MC? It really depends on the character. He or she may be crushed for weeks, barely able to get out of bed and eat. He or she may cry for a day and then be able to get on with their life, still with that ache in their heart. The character could become bitter and angry, not mourning at all. Depending on the situation of death, the MC could deny that their close friend/family member/etc. really died. The possibilities for this are endless. My tip for this is to know your characters.
2. They are physically injured.This does have an emotional impact on the character. The MC could have cancer and be slowly dying. That would sure impact the MC's emotions. He/she could become really depressed, sad, angry, or try to live out his/her last days to the fullest. Think about Frodo in Lord of the Rings. Not only did the Ring have physical effects on him, but it affected his heart. He became attached to the Ring, even though it literally became heavier.
3. Basic needs are taken away.
Yes, this is something physical, but it also has an emotional impact on the character. Will he or she become inhumane and eat anything? Will he/she be scrounging for water and ditch his/her family? What is he/she feeling?
I only covered a couple of the ways that you can impact a character emotionally. There are many other ways. Just remember that it is important that things hurt your character for them to grow in the end!