This series is riddles with tragedy.
However, there are certainly some that have touched me more than others. Here is the shortlist of what I consider the greatest tragedies of the series, in no particular order, sharing some of my thoughts on each.
1) Jon Snow and Eddard Stark.
One of the two things about Eddard's death that saddened me the most is that he now never gets to tell Jon the truth. Imagine the beautiful scene that might have been had Eddard ever believed it was safe to tell Jon that he is not actually Jon's father (yes, I am a supporter of R+L=J), that he is Lyanna's son, and that keeping the secret was Lyanna's dying wish. The only person alive who still knows this is Howland Reed, and I'm sure the scene where he reveals it to Jon will be powerful (note that I also think Jon is not dead, or not staying dead), but how much more powerful would it have been coming from Eddard?
2) Jon Snow and Catelyn Stark and Eddard Stark
The other thing I find saddening about Eddard's death, is that he will never get the chance to explain to Cat who Jon really is. Although the sudden burden of knowing that the hatred Cat had borne Jon all those years was for nothing, the potential for a strong family bond was there as well. Not only is there so much lost drama between Ned and Cat as she comes to grips with him keeping it a secret from her all these years, surely she would understand his reasons for doing so, knowing her husband's devotion to honor; but then there is also the lost drama of Cat trying to apologize to Jon for antagonizing him all of his life.
3) Maester Aemon and Daenerys
I wish very deeply that these two could have met. Aemon could have taught her so much about her family and her past that she has lost, and could have seen in her so much hope for the survival of his family. It would have been so good for both of them. Especially since the only Targaryen that Dany had known in her life was "less than the shadow of a snake."