Sniper and Spy seem to be widely shunned in MVM as useless classes that cannot help the team in any meaningful way. Some have no good reason. Others throw around claims like, "Sniper doesn't do enough damage" or "Spy dies too much", but these are often just attempts to justify their contempt for these classes. Here, I will explain how a good sniper or spy can be useful to your team, and why you shouldn't immediately call a votekick as soon as one joins the server.

In a game of MvM, the spy can do several useful things. First, he can take out Uber Medics. If your team lacks a stickybomb demo, a Spy can be a suitable replacement. Second, he can sap robots, stunning the regulars and slowing giants. He can take care of snipers, engineers, and other spies, as well as stab giants with his armor piercing upgrade for massive damage. He also serves as a distraction and a cash collector.
Also: little-known fact here.
The Spy reveals cloaked Spybots near him.
This means that cloaked Spybots 'flicker' like they do when bumping a defender when a human Spy is near. This is a very useful ability wherever Spybots can be found.

But he dies way too much!
This is to be expected. The Spy is up close and personal, he's bound to die often when things get hectic. But his job is still important. With the ability to take out large groups of robots quickly, and distract giants, the Spy is quite helpful, allowing his team to deal more damage for less risk. His death is not as important as yours; his handiwork can buy him enough time to get back in there and start sapping again.

The spy's disguise always fools robots until they touch him or he is set on fire, so he can remain undetected by the horde. They also ignore uncloaking right in front of them, so he can use his Dead Ringer to protect himself and keep the robots occupied. The Spy can also use Ammo Canteens to instantly recharge his Sapper.
Weapons

Primaries

The L'Etranger
A good tool, this weapon will allow the Spy to recharge his DR while escaping. It is not, however, very useful against Razorback snipers.

The Ambassador
Good for spies with good aim, this weapon is particularly useful against Razorback Snipers.

The Revolver
Good all-around escape weapon. Nothing special, though.

The Diamondback
Can be very useful for Spies who stay alive for long periods of time, but the crits are often wasted for most spies. Circumstantial weapon.

The Sapper of choice doesn't matter, the effect is the same on robots and when it comes to Engineer-bots, it is a matter of preference.
The only good watch in MvM is the Dead Ringer- the Invis Watch and especially the Cloak and Dagger are simply bad, as you already have 'invisibility' with the disguise kit.

Knives

The Butterfly Knife
The safest knife, this one can be upgraded with Health on Kill to keep the Spy in the fight. Swing speed is particularly useful for larger crowds of robots, and the Armor Piercing upgrade allows more damage against giants.

The Conniver's Kunai
Actually not that useful, the Kunai can be good early on, but the health penalty combined with its special ability which is already gained with upgrades, the Kunai isn't that great.

The Big Earner
An all-around nice knife, the Earner allows you to chainstab some robots and escape with your DR more quickly.

The Your Eternal Reward
You'd think this would be good, but if you have the DR equipped it's near-impossible to get a stab in with the robots' x-ray vision. Even if you get a stab, you don't get the robots' disguise, as it only works on human players.

The Spycicle
Otherwise identical to stock, it suffers when Pyro robots are around, because although you'll become immune to the afterburn, you can't stab again for a while. Not too good, since you'll need to be there when the next swarm of robots inevitably appears.

The Sniper stays far from the field of battle, popping heads left and right. His ability to damage robots from such a distance makes him an incredibly powerful combatant. His sniper rifle can do a lot of damage to a lot of robots very quickly with explosive headshots, and there is no better class for taking care of the bomb carrier. His damage output allows him to wreck giants and He can delete snipers and demolish Engineers and their buildings, plus he can slow down the robots with his Jarate and give the team mini-crits. In addition, the Sydney Sleeper can still deal explosive headshots.
But he doesn't do enough damage to matter!
I don't know from what part of your a** this notion was pulled. The Sniper deals more damage to giants than any other class does, provided he can land headshots. At maximum upgrade, a fully-charged headshot from the Sniper Rifle deals 900 damage. Combine that with an upgraded charge and reload rate, and you've got yourself a killing machine with more damage than he knows what to do with. It may be surpassed by some classes for very short periods of time, but the Sniper can stay well out of range of the giants, where he cannot be harmed by them. Thus, while your Soldier, Demo or Heavy may die, the Sniper can keep on truckin' with his hunting rifle of robotic doom, safe from harm.

Additionally, with an upgraded Bushwacka, the Sniper can deal full crits while buffed with the Buff Banner, allowing him to kill tanks more effectively than if he just no-scoped the tank. The Sniper can be a valuable asset when dealing with powerful Giants that can kill anyone who gets too close. The Giant Deflector Heavies in particular are especially weak to Snipers. Bonus points if they're critboosted.
Weapons
The best secondary and melee are probably the Jarate and Bushwacka- other ones are very selfish items that don't help your team, which is important in MvM.
Primaries

The Sniper Rifle
An old and reliable weapon, the Sniper Rifle is, like most stock weapons, good all-around.

The Machina
A powerful gun able to do increased damage on full charge, it can be useful for burst damage but it cannot be fired from the hip, making it harder to defend yourself when robots show up next to you.

The Hitman's Heatmaker
Possibly the best sniper rifle for an experienced Sniper, this weapon can deal much more damage than the Machina, provided its user can land consistent headshots. A very good Sniper can even keep their Focus going, making sniping large quantities of robots or getting multiple consecutive headshots on giants easy as cake.

The Sydney Sleeper
An underrated rifle, this one can be useful for helping your team. With the ability to Jarate multiple robots and an inherently faster charge rate, it offers a free upgrade at the cost of headshots. However, explosive headshots still do work on this weapon.

The Hunsman
Not a very good weapon, it suffers mainly from the lack of explosive headshots or some kind of splash damage- MvM mainly being about fighting large hordes of robots, the Huntsman suffers in this aspect, but it can still be useful if you're very good with it and your team is good as well.


For this, I have video evidence. If you require moar proofs, watch this instructional video.
I take no credit for this video; it belongs to British Dominance.