For such a simple question the answer is actually difficult.
If we set aside our personal desires re: dead or alive, and look at this objectively the most simple answer is undoubtedly the most accurate. Is Ichigo dead or alive? he is the same as he's always been, both.
Ichigo was born of a human mother and a shinigami father (as are Karin and Yuzu) so from the moment of his birth he has been both dead and alive. While the cannon states that a soul is considered dead when the chain of fate is cut, and Ichigo's was so that should have 'killed' him, however Ichigo is special, he was born half dead already, so from a non biased point of view, the chain cutting aspect doesn't make him any more dead than he already was.
Death in bleach is a very hard thing to quanitify because, well its a story about the afterlife, or living after death.
So what do we define death as then?
1)Is death when a soul ceases to exist, as is the case when its destroyed by a quincy?
2)Is death when a human body dies, ejecting the human soul to float around the real world with a broken chain, waiting to receive a Konso or decend into a hollow?
3)Or, would death be when a soul is Konso'd (or purified as a hollow) and enters Soul Society?
These are all examples of "death" in bleach, and as far as i know each is considered accurate. So which of these applies to Ichigo then?
None of them do, even after his chain was cut Ichigo has continued to age normally, and use his body normally, so that means that aside from gaining access to spiritual powers, he is no diffrent now than when he was when he was born. Essentially, due to his unique parentage the 'normal' rules shouldn't apply.
In the first post, Detergent asked what makes Ichigo diffrent from Byakuya, Rukia and Renji, well lets explore that question in depth.
We know that Byakuya was born, in Soul Society, never having been 'human'.
We also know that Rukia was born as a living human and died as an infant and entered Soul Society that way.
So what makes Rukia a dead shingiami and Ichigo a living human?(the entire cast calling him human means Kubo considers him human) They were both born as humans and they both through different means, had their souls removed from their bodies and their chains severed. (Rukia's from death, and Ichigo's from Urahara and Tessai).
So at the most basic possible level, these two should be equally dead, right?
But they are not, the difference between Ichigo and any other 'dead human' like Rukia, is that the dead humans have passed over into Soul Society, they entered the afterlife, Ichigo has not undergone this process yet, hence why he is still considered a living human.
In the broadest possible meaning, being dead means that you are "from" the afterlife (Soul Society/Hueco Mundo) Byakuya was born in SS so he is from there and is dead, Rukia died as a human and entered SS as a soul, so she is "from" Soul Society and considered dead.
We have seen that when a 'dead' soul from the human world is Konso'd, they vanish by some unseen means(the spirit king?), lose their chain of fate and reappear/reconstitute inside soul society, having no more ties other than memories to the human world.
This is what I am considering being dead in bleach, this unseen process of a soul being taken out of the human world and placed into soul society, no longer having a chain of fate. Purified hollows also fall under this category since they 'dematerialize' (for lack of a better word) after being cleansed by zanpakutou. (though its not actually been shown, its heavily implied that the hollows soul is sent to soul society)
We know that Ichigo is special, however, no matter how special he may be, the basic natural laws of bleach have to also apply to him, otherwise he would have stopped aging as soon as his chain was cut, so from that view, and since his soul has not entered Soul Society through "death" we must concede that Ichigo is still alive and human, but also equally concede that due to the shattered shaft, and/or his father, he is also dead and a shinigami/hollow(yes he is a hollow he dosnt have a hollow).
So, Ichigo is both dead and alive. (as of ch518)