it doesnt have to ba a major character... but it can...
basically, whichever character that might have showed showed up for a certain season or a single chapter that got killed off, and you were attached to that character....

for me it was ...

Death Note :

L dieing was pretty saddening for me

Elfen Lied :

I wished Nyuu/Lucy didnt die that way :(

Naruto :

Itachi, which was pretty saddening

Claymore :

when that women that took care of clare died by getting decapitated,,, which was soo saddening

Bleach :

that black espada in the recent chapter, with the big boobies.... i was like,, noooooooooooo, shes too hot to die

I agreed with Death Note, I was sad too.

My favorite characters always seems to get themselves killed, so I can't remember all of them. Here is a recent one, though:

Ares:

The guy with the spear, right when he thought he finally was going to lead the life he's always had wanted Michael showed up and killed him for the heck of it...

I believe this is basically a repeat:

Most Heartbreaking Scenes