We muggles tend to think of spells as things like bullets traveling through space, following laws of physics like ballistics, to affect a target, but that's not what spells do. Spells "adjust" the laws of physics to the will of the wizard, allowing one to light a candle, or levitate a rock, or travel through time.
With practice, a wizard gains the ability to apply more "will" behind their spells and have greater effects. The "more powerful" wizards are those with the experience and charisma to impose their will and intent on the universe.
One constant I've seen in Harry Potter spells is the need for "Intent." Barty Crouch, Jr, states that the spell Avada Kedavra requires "a powerful bit of magic" to power it. Snape claims you need "nerve and ability" to cast unforgivable curses. It's not good enough to point and say the words, you have to intend for that curse to kill somebody (or harm them).
So, a spell isn't a bullet being shot from a gun; a spell is a wizard or witch bending reality with the force of their will. They INTEND to make something float, they INTEND to light all the candles in the hall.
They INTEND to make that spider die.
It all comes back to Barty saying that everyone in the room could point their wands at him and say the spell, but it wouldn't harm him. It's not a bullet guided by the laws of physics, it's the will of the caster bending the nature of the universe to fit his desires. I imagine a sufficiently powerful wizard would be able to kill a spider, but not kill a human, or kill a human, but not through clothing (his intent not being powerful enough), or to kill a human through clothing but not armor.
So, I would say, Unfortunately for Voldemort, Avada Kedavra (as currently known by the wizarding world) is not an instantaneous curse, but instead a curse with a travel time and line of sight. This is what saves Harry Potter; when the statue intervenes, Voldemort's INTENT was to kill Harry Potter, but the spell never reached him, and instead struck the statue.
Had the spell hit Harry's clothing, or armor (if he was wearing it), the INTENT would have still been the same: killing Harry Potter. And Voldemort would have enough force of will to impose that end result on the small "distance" between the actual landing of the spell (clothing) and the person being cast upon (Harry).
But because Voldemort BELIEVES that Avada Kedavera needs line of sight, and must touch his target, the spell fizzles.
I imagine a sufficiently powerful wizard, such as Voldemort or Albus, may be able to impose so much will on the universe that striking a container, such as a wooden box or an armored vehicle, inside which resided their INTENDED target, would still cause the death of their target inside. However, I would also suspect that less able wizards would find increasing levels of armor (kevlar, plate armor, plate armor with a shield, armored vehicle, etc) increasingly difficult to apply their effect to.
As an alternative explanation, building on INTENT as the driver of spells, if Voldemort believes that a statue can block the spell from reaching the target, his INTENT to kill Harry Potter with the spell evaporates when it misses. We, as humans, expect causes to directly apply to that which it effects; it could be the same for magic.
In this case, a sweater or suit of armor would not impede the INTENT of the killing curse, but if Harry were to sufficiently convince Voldemort that his Unobtanium-weave Kevlar armor absorbs and blocks the effects of spells, Voldemort would work on hitting unprotected parts, and would therefore lose his force of will when a spell hit the kevlar.
There is some speculation here, and it's a bit hand-wavy, but JK seems to see spells as affecting "objects" not individual components, or affecting "people as targets," not affecting things like hats and glasses. Unlike westerns, where guns are repeatedly shot out of hands, it appears that spells in the Potterverse are really directed by the intentions of their casters.
