From TF2 Wiki
The Rush is a strategy involving the entire team or majority of a team selecting a single class, and using that classes' strengths or the shock value of the strategy itself to steamroll over the enemy. These will typically be ineffective without coordination and the surprise element and are only likely to work once on most maps. When used effectively however, they can ensure a quick and decisive victory.
Rushes by Class
See Scout rush
The Soldier rush is quite deadly at close to medium range with an entire volley of rockets being harder for the enemy team to dodge. Your shock tactics and high mobility may allow you to steamroll over the enemy for a quick and decisive victory. A Soldier rush can be foiled however by a combination of sticky bomb carpets, Snipers and/or Spies. Also without Medics on hand, your Soldiers will suffer high damage that is unlikely to be healed, though Equalizer's will substitute for that to kill off distracted opponents. Pyros setting multiple Soldiers on fire or reflecting rockets can spell doom for the rush. All in all, the Soldier rush is a "do or die" tactic, where you will either win easily, or die quickly. Some Soldiers will carry Buff Banner's to aid the assault.
The Pyro rush can be an effective tactic in some cases, but is ineffective in most. While a high number of close range attackers with disorienting fire damage can leave a team in chaos, you are also in deep trouble if you should encounter a Heavy/Medic pair with a ready ubercharge (highly likely at the end of setup time) who are likely to mow you down before you can deal serious damage, or a single higher level sentry which can stop you all in your tracks.
A Demoman rush or Demo rush combines a solid defense with strong offensive capabilties, with volleys of stickies preventing the enemy from moving forward or even leaving the gate. However, capping points will be more difficult unless the Demomen are skilled in aiming their less directly accurate weapons. If they manage to get on point and booby trap the entrances to the area then they can weather a sustained assault. It is one of the few class rushes that is able to overcome an uber pair. However, the rush is vulnerable to Spies and skilled Pyros. Many Demo rush's consist of the team using a combination of Sticky bombing Demos (Using either the regular sticky launcher or the Scottish Resistance) and Chargin' Targe Demos.
The Heavy rush is a tactic where you use the superior health and firepower of multiple heavies to create a steamrolling vanguard few teams can withstand. However, with low mobility and the absence of medic partners this can prove a risky tactic. Eventually, the enemy is likely to overpower you and your slow speed may prevent you reforming the vanguard before the enemy have set up stronger defences. On an unprepared foe this tactic can be devastating, though they are likely to be prepared a second time, and counter.
The Engineer rush is normally ineffective except in specific circumstances. If the Engineers all equip a Sentry gun ready to lay down and can all start them building at the same time while switching to the shotgun this can be effective. Engineers lack high direct damage attacks and sentries take time to build, so mobility is hampered and an enemy ubercharge can cripple your rush at setup time. If a window of opportunity arises however, a line of sentries can be set up to take out incoming enemies allowing you to push forward if the enemy team are scarce, though ultimately this is still less effective than a well-balanced team. This is far more effective on defensive maps and games such as the red team in payload maps, and it can also be used for more effective turtling.
The Medic rush is a tactic where you have an entire team of Medics paired with other Medics. If you can make sure half the medics have Blutsauger's and half Mediguns, this will make it harder to kill individual Medics. If all the armed Medics fire at once it can create a volley of syringes that will be difficult to dodge, along with a succession of ÜberCharge's which can make for an almost unstoppable assault. ÜberCharges neccesitate a high level or coordination and teamwork however, and once they fade out you will be left vulnerable. This can be effective for capping individual points however.
A "Medic Rush" can also refer to half of the medics using the Ubersaw while the other half charge them. This is useful because it can refill the ubercharge spent by one medic, and the medics can afterwards change place and continue attacking with another ubercharge. But a downside is that the Ubersaw is a melee weapon, making it difficult to hit opponents. But when it does, it is deadly.
The Sniper rush is very rare. Unless your whole team can aim extremely well, it will likely fail. If your team is made up of effective players, then a Sniper rush's biggest impediment are fast classes, Sentry guns and Spies. The Sniper rush is most effective on maps which maintain large stretches of open space. Maps with tight choke points or an abundance of corridors can cripple the Sniper rush.
The Spy rush is an uncommon tactic. It involves a large number of a team becoming spies, then disguising as various classes and rushing the enemy base. If used correctly, then the Spies can sow confusion among the ranks. It may also allow the Spies to take down well-guarded turrets with the advantage of numbers and a larger supply of constant sappers. A successful Spy rush may well give the Spies' team an opportunity to slip past the group hysteria and proceed with the fulfillment of the objective. Pyros can spell death to this tactic however.