As a player, having a character die due to a die roll - after spending a week or so developing them, being excited about their potential, and immersing myself into this character's life, skills, and relationships - I would be pissed. And I know it's a game, and that death is sometimes the way it goes, but i myself absolutely Do Not believe dice should dictate life. You don't need death hanging over a PC's head to instigate chance or fear. Players should not be thinking 'if I don't succeed, I am going to die'. They should be thinking, 'If I don't succeed, the bad guys will win'. Death itself should be a non factor.
I'm not saying I believe you should never kill characters. What I believe is that death itself should be in the player's hands. They are the ones invested into the character, they dreamed up its creation and have planned or imagined its future. They should be the ones to decide whether to terminate the investment and start over, not anyone else. Player stupidity should definitely not be awarded - if they ignore warning signs, or grossly overestimate their own abilities, etc they should definitely pay the price. As a GM, there is usually something else you can choose other than death. In the deer example above, my choice would have been to make the PC unconscious and give the player the chance at an outcome roll. Assign the roll a few possibilities - loss of use of limb, infection/rabies, loss of ability, death - allow the player to remove the death option if they want, and then roll. The character's fate is still up to chance, but the player has had the opportunity to remove death from the equation.
If you have a character that falls into death situations on a regular basis, then you have a problem, but that is a deeper problem than death via die roll, and is another discussion entirely.
Of course, this is the point of view of a person who has played tabletop maybe 4 times in her life, and joins game to participate in the story rather than try out the new ninja rules. If i join a game, I expect to be immersed, for my character to establish relationships, fears and desires, and experience danger. I expect my GM to engage me and communicate and not pull a cheap shot, like rendering my character dead instead of crippling them because they fumbled a climb or jump roll.
Also, I try not to play games where I know the GM practices death via dice. I played one once, and I didn't like it at all. I found myself always taking the safe route, never reaching for chance or RPing my character to his full capacity. If there was a way to do something without I dice roll, I opted for it. The character itself was a thief, with high acrobatic skills for scaling buildings. Ask me how often I stole, or climbed through a window, walked across a rooftop - zilch. I was that paranoid to roll. And I'm sure the GM was as disappointed in me as I was, and it won't be an experience I enter into again. No matter that the GM is stellar, that I admire them, and am inspired by their writing. I know that there is a chance my PC can die in a routine battle, and I know how pissed I will be if that happens, and how I would be mad at the GM even though it really wouldn't be their fault cause it was my choice to enter the game in the first place.
In my current 4e game, which is more a GM experiment because people keep trying to convince me I will like 4e, I am GMing seasoned players that are accustomed, and actually prefer, to have death as a dice option. It's a foreign situation for me, and I still can't bring myself to allow it, so I have come up with this solution: If a character or NPC rolls a death card, they will get two outcomes (posts) from me. One will be their death, one will be the other, and they will have the option of choosing between them or rolling a decision die. I think it's a fair compromise.
On the fudging rolls or manipulating battles, I've done it a few times. The first time was a tourney style fight whre the opposition was supposed to be cheat. While the player and combatant battles, a pair of overhead archers was overhead to strike at them with arrows, blunted with sacks of colored powder, as a distraction and to inflict some minimal damage. In the event the fight wa a close one (we went rounds, not until hp reached [x]), the winner of the contest would be the one wearing less powder. Since the opponent was cheating, my archers were only going to aim for the player, so I wanted them to only be able to hit on a natural 17+. Trouble was, I'd forgotten one of the character's buffs so my archers couldn't even hit with a natural 20. So after the first round, i upped their BAB. i did inform the player, and he laughed at me.
The second time was a chamber with a pit, the pit being magically dark so the PC couldn't determine its depth, and the chamber entered and exited via doors locked by puzzle. A bridge ran over the pit, connecting both doors, and elements to finish the 'exit' puzzle were needed from the 'enter' puzzle, so the PC had to go across the bridge at least once in figuring it out. Two shadow panthers jumped out of the pit to oppose him. He dispatched of these easily, without hardly losing any hp, so I decided that the shadow panthers were regenerating guards and hopped them out again. In the end, I had to allow the PC to figure out the puzzle with one less puzzle piece in order to let him get away from my panthers, but it was a highly enjoyable confrontation, both for myself and my player.
The third time was simple 4e newbness. I am used to leveling up monsters in relation to PC BAB/talents/etc. I discovered that when you do that with 4e monsters, it is not such a good thing. It was my first 4e battle, one PC vs 4 thugs, 3 on the cobbles, one on the roof. The rooftop archer kept hitting and rolling max damage. The leader hit him with a crit, and in one round, the PC was depleted of 54 hp. I completely abandoned the foes hp altogether and had the lead thug die in the next round, the two on foot run off, but kept the archer - who continued to roll max damage - until the pc got up there, and then i had the archer beg for his life and when it was spared, made him a valuable NPC as a whim.