While trying to by systematic in my response, there's a number of things I need to address.
1) the use of 'favourite': this is hard because i don't really have a favourite character amongst all the series i've watched. I think each series has its own special character that has totally captured my heart and my imagination. So because of that I'll list a few in this post

2) on Dying: some of my favourite characters from different series already have died, for instance there's Spike from Cowboy Bebop, Kenshin from RK (that's if you count the final OVA as being part of the canon) and Maes Hughes from Fullmetal Alchemist.

3) to finally answer your wonderfully thought-provoking question on how I felt when these characters died: My immediate response would not be unlike the other participants of this thread; I was sad and in most cases I teared up. But after the moment passes, and I look back at the series as a whole and how that character death has contributed to the overall narrative structure, I more often than not, find myself glad that it worked out that way.

I think character deaths provide very powerful moments in a series. Whenever an author has the courage to kill off a favourite character (without bringing them back as part of some cheap trick due to popular pressure) or permanently maim/disfigure a character. I think it sends out a message that life is not always beautiful and not always perfect. It deviates from the simple and the easy which is finding and appreciating beauty in beautiful things and forces the reader/audience to look and see the beautiful in the ugly. Our aesthetic appreciation of the character is heightened and deepened. We no longer like a character for his boyish good looks or his/her wonderful physique and beautifully styled anime hair, but rather for the backstory behind the character. The internal struggle that the have faced and the internal strength and beauty of the character.

But I digress. I'm focusing more on maimed and disfigured characters rather than character death.

To get back on point, I think in the three cases that I've listed, I thought each death scene was powerful and meaningful. I'll briefly elaborate now and hopefully those who are familiar with the respective animes will respond and we can have a lively discussion going, aye?

Spike I thought would have been better off dying at the end of the anime because he was so trapped by his past that he had no way of carving a path for his future. His character seemed to be trapped in limbo, a kind of purgatorial state throughout the series that death seemed like the only viable resolution for him. At least in death, there would be some semblance of peace and closure for him.

Hughes' death scene was fantastic. I think it raised the whole series to another level. It cemented the militaristic, war-like atmosphere that permeated FMA and made it real... or at least as real as it ever gets in an animated series. Things I loved about Hughes' death scene was the suddeness of it and how there was no warning. There was hardly any time for mourning after it either. It captured the brisk and impersonal nature of all this war-business. I thought it was just lovely. Of course it was bittersweet though. I appreciated its strategic significance as part of the narrative but it was heart-wrenching at the same time to watch.

As for Kenshin however, I wasn't so satisfied with it. Personally I don't consider OVAs and filler episodes that are not part of the manga as part of the canon storyline. So the final OVA for the RK series for me felt a bit like the producers were just milking the storyline and the fans for all they could get. So not too happy with that.

4) as an additional category, characters I wouldn't have minded dying: if any of you are familiar with the first season of Fullmetal Alchemist, I seriously expected Edward to die in the last episode. But I thought the trade off at the end was good too. It was a high price to pay for both brothers and in some sense it might be a fate worse than death, except that they are both still a live...

Yup. Sorry for the long post. I tend to get very excited about these things. Do reply! I look forward to your responses!

Well, I'm having a hard time seeing Gin's death in my mind. To me he's just so invincible....

I'm also having a hard time picturing Hirako's death. I can see him get beat up, but dead... no.

Hitsugaya used to be my favorite and I thought he couldn't die, but after he keeps having to time after time use his Bankaii, I feel that he's weak. For a captain, that is.

But I love all the Bleach characters. Well, almost all.

You can't imagine shiniji dying? While it's saddening and depressing to think about, but i think Ichigo's relationship with shinji is comparable to the one naurto had with ero-senin, and the frog man died. My favorite character is Ichigo's dad and urahara. I don't think ichigo's dad is important enough to die, i mean it would serve no real purpose to the story at the moment. And if urahara will never die, ever.

But Bleach has seriously need to kill off some characters. It has such a ridiculously huge cast that the mangaka seems to have trouble juggling them around. Personally i'm really bored of the 4th captain and the two kids at urahara's shop makes good target pratice for Stark.

Btw, i got really pissed when Shirley was killed by Rolo, but that's because Rolo wasn't even suppose to be a fking character if the time slot hadn't changed, so Shirley died for NOTHING. And i cried a little when Lulu died.

Come to think of it, i think i get a little teary when most characters die. =0

Mine fav char is Ichimaru Gin and according to Manga/Anime he will die for sure since hes "the bad one". Well, i hope he wont ~~

I can't picture Shinji dying because he's not serious. A death scene in Bleach is always dramatic to the greatest extent (which I like) and to see Hirako being serious?!

Very hard to picture.

Plus, I think that Gin is either going to die in a dramatic way where you can't see a crap that happens, or he's going to surprise us once more and turn out to be a good guy? Who knows?

I just hope that if any of this actually happens, that it's a good 4-8 hundred chapters in the future.

I cried all night... like what happen to Shishio Gen (kekkaishi) i feel like something missing... like a real death... weird, but that's love XDD

I get that. I hate it really, that I can feel so sad when one of my favorite characters die.

Oddly enough... I felt little remorse when Ulqui died.

I actually don't know how I'll react if one of my faves in Bleach dies xD I will get depressed, I know that, lol.

But when L died, I got over it fast, but since I like my fav characters better than my faves in Death Note, I think I'll react more, and be more depressed, but who knowes x)

When one of my favorite characters dies I usually cry, and if the series goes on after their death, I get a little sad that I won't be seeing them for the rest of the story. It's so depressing. But the good thing about anime and manga (and most forms of fiction) is that when the story is over, you can go back to the beggining and see them again. Or you can look for fanfiction where they are alive and happy, or write something of your own, whatever helps you cope.

Anyway, in Bleach hardly anyone dies (not counting the fact that most people are already dead there), so it doesn't worry me much. However, when they do kill off someone and it's someone you like, it'll suck double because it so rarely happens, and when it does, the one to get it is the one you wish would stay alive. Beyond unfair.

I'll maybe stop watching the anime XD and get totally crazy

I would be utterly sad and feel very bad if one of my favourite characters die in Bleach but on the other hand i have nothing to worry about because KON is my favourite character in Bleach and he cant die because he is the real hero of Bleach, heheheeee

Well my fave is Hitsugaya and I think I would just go:

Noooooooo -echo- -echo- lol XDD

I do not know about that i wood do mad if Ringo from Air Gear was in front of me that girl is hot

What you should do is pick someone which is not going to die like ZARAKI :D

I'll cry and feel sad. I'll think "That's true? I don't believe it!" It's like, you'll lost your best fantasy friend.