What are the advantages of using the Huntsman?

I have recently acquired the Huntsman when playing as a sniper and I have been wondering why should I use it in Team Fortress 2, other than completing some Achievements.

Specific advantages:

1. Faster charge time.
2. You can fire into a passageway where you suspect an enemy is about to appear, and unlike an instantaneous shot the arrow has a much higher chance of hitting someone, simply because it's around for a longer time.
3. Deadly taunt :)
4. Leaving arrows sticking out of enemies is awesome.
5. You can launch flaming arrows! Just let a friendly pyro or soldier with the Righteous Bison shoot you while pulling back the string.

In general, the bow is better for shorter ranges. If I'm holding a rifle I can usually counter-snipe bow-using snipers easily; on the other hand, defending cramped spots or running along with other attackers is far easier with the bow. It's really a weapon recommend for aggressive snipers.

In my personal opinion, a bow-wielding sniper is nice but it's not the truly scary thing thing a good rifle-wielding sniper is, and I only use the bow in specific situations. Not that I say that the bow should be underestimated, but the rifle:

1. Is easier to hit with, in my opinion, because of the instantaneous bullet.
2. Has a potential for higher damage.
3. Is much harder to dodge.

... so I prefer it.

In addition to the advantages that Oak posted:

1. You have a greater field of vision due to not being scoped. You'll be less likely to miss that spy creeping up behind you or the soldier firing rockets in your face.
2. Much easier to quickfire in frantic situations. Being able to fire against a slow moving target (like a heavy) and retreat behind cover in a split second during recharge is incredibly advantageous.
3. Similar to 2, taking out sentries when you're stuck in range I find to be much easier.
4. Distinct "thwack" sound when you successfully hit a target. Cant count the number of times I've blind-fired into a group of teammates, heard a "thwack" and instantly known that there's a spy in there.

And in addition to the disadvantages:

1. Smaller ammo capacity, 12 vs 25.
2. Arrows CAN be compression blasted back in your face by a lucky / skilled pyro.
3. You cannot fire your bow underwater. This makes snipers who decide to use Jarate / Razorback (which is most of them) and the Huntsman practically useless and defenseless if going in the water.