What is the most effective way to counter a Sniper?

There are 3 general ways to deal with snipers:

1. Become better at dodging/avoiding shots. Learn and use terrain to get out of the sniper's view, and also adjust movement to make it difficult to snipe. Don't just run in the open from point A to point B.
2. Spying. Spies are unrivaled at harassing snipers. A good spy or two will keep snipers constantly spy checking and unable to spend time zoomed in. The Ambassador will take care of those Razorbacked snipers just fine. Also, don't decloak right behind a sniper. It's usually fairly quiet next to a sniper, so its really easy to hear a decloak. To be fair, to go with the tons of bad spies that do this, there are tons of bad snipers that are caught with this. Maybe they should turn down their music?
3. Counter-sniping. Simply be better than the other sniper. Lock down the other snipers, AND rain down on the other team. Snipers are their own counter.

People such as soliders and demomen never really bother me as a sniper. I see them coming, and a demo will be mostly dead if not already dead on the way down. Mid-air is a great place to shoot people at that. Scouts are annoying, but them along with any class should generally have a rough time getting to you past your team to be a regular issue. Other classes really shouldn't be reaching you.

Spy, Scout, and Pyro can all be effective, but the class most hated by the best sniper I know (the ridiculous Flippy_D) is actually the Demoman.

Backstabs can be handled with the Razorback. Pyro and Scout by being aware of any back door, but the Demoman has long range, and can easily spam a Sniper's camping spot, at worst keeping him from getting off a good shot, or even killing him. Additionally his damage does not decrease by distance like the Solder does.

Well, there's a few things I really hate as a sniper. (Keep in mind that although I do have my moments, I'm not an excellent sniper by any stretch of the imagination, so you may wish to take this advice with a grain of salt.)

1): Enemy classes getting into my sniping spot. Nothing irritates me more as sniper then being blindsided by an enemy while I'm looking for headshots. There are two ways to do this. You can either just rush me (scout, or a rocketjump/stickyjump), or sneak past my sniping spot and flank me (which almost any class can do, if you know the map.)

2): Better enemy snipers Yep, the biggest threat to a sniper is another sniper. If you're faster and more accurate, enemy snipers can be some of the easiest kills in the game. (Probably not what you're looking for, but I thought I'd mention it) Also, try sending some rockets/flare gun shots/ stickies towards my hiding place. When I'm scoped in, I don't always notice, and you might get an easy kill.

3): Zig zagging enemies As a sniper, what's harder to headshot? The guy that moves in a straight line towards you, or the guy zig-zagging, bunny hopping, just meandering randomly all over the place? Move left/right and up/down in addition to forwards and you'll reduce your headshot deaths a lot.

4): Spies These deserve a special mention. Although rushing/flanking enemies can be held off if the rest of your team is playing well, often a spy can sneak past them anyway, and just backstab me. Don't be afraid of razorbacks, as a couple of revolver shots will do the trick nicely. (Although, since most spies tend to shy away from razorbacks, I use the item anyway. :P) As a side note, the headshot hitboxes of each class are indeed different, so it's tricky to headshot disguised spies even when they're obviously enemies.

So, which class would I use against an enemy sniper? (Assuming I couldn't outsnipe him)

1)Spy: Snipers are the easiest backstabs in the game, if you can get to their hiding place. Which equipment you use is a matter of choice, but the ambassador can be excellent against snipers (They stay very still when scoped, making for some easy ambassador headshots).

2)Scout: You're vulnerable to charged bodyshots, but you're very difficult to headshot if you move around erratically, and you have a good chance at reaching their hiding spot. The force of nature helps by allowing you to triple jump, and bonk atomic punch will let you rush past enemies to get there. Also, the sandman has a shot at some ridiculously long range stuns.

3)Soldier/Demoman: These are purely for the additional movement allowed by rocket/stickyjumping. You can really zoom around the map when you use it correctly, which can really surprise a sniper. I'd suggest the default kits for both of them (aside from equalizer for soldier).

Other class ideas: Don't even think about heavy unless you're planning to use the fists of steel. Also, brass beast is a HUGE mistake. The movement penalty makes you a sitting duck.

The engineer doesn't have too much long-range capability, although a wrangled sentry is definitely a possibility.

Medics are a high priority target for snipers, although the crusader's crossbow might work.

And finally, flare gun pyros can nail inattentive snipers. Don't forget to use your flamethrower when crossing open spaces, you can mask your head in the flames to confuse snipers.

Well, that's all of my experience regarding sniper hunting, hope it helps.

The three classes most suited for killing Snipers are:

1. Snipers. Some maps in particular are very Sniper-battle friendly at the beginning. Most payload maps are a good example (see: pl_goldrush stage 1, pl_badwater, pl_upward). Pretty much all maps are sniper battle friendly in the middle.
2. Spies. Even with a Razorback, a Spy can just shoot you 3 times (twice with the Ambassador, assuming the first shot is a headshot) to kill you.
3. You wouldn't think Scouts would be, but it's easier for them to get past Snipers due to their speed.

If you must engage, go pyro with flaregun or scout with the sandman. These classes can get close to a sniper.

If you go pyro, remember you can just spray flames around and strafe randomly to make it harder for them to hit.

If you go scout, well, then you are really fast. A sandman hit (or even a miss) might scare them away from their spot. You can use either a bonk or a shortstop after having used the sandman. It will be hard for the sniper to counter the fact that your bonk makes you invincible, and the shortstop is massively overpowered.

Many people would probably recommend a spy. Here is my opinion: A spy can often take out any single target, but will it be worth it? Remember it's called Team Fortress. Taking out one man is not a sensation.