Rushes are strategies, usually early-game, that use speed, surprise, and numbers to win. They are effective early-game, because the enemy will not have had time to set up a proper base and their defensive capability is minimal.
Allies
Vindicator Rush — This tactic is available early on for the Allies. Just build a Power Plant, then an Airbase, purchase the Advanced Aeronautics upgrade from the Top Secret Protocols menu and finally build as many Vindicators as you can and send them to level the enemy. This is ineffective against mass Flak Troopers and against enemies that have Mecha Tengus, although you can strongly minimize the Tengus' effectiveness by ordering Apollos to escort your Vindicators. One upgraded Apollo can hold against three Tengus simultaneously.
Peacekeepers and Javelin Soldiers — This is another tactic useful against an unprepared opponent as long as the enemy does not deploy vehicles to crush your troops. Use the Peacekeepers for enemy infantry while use the Javelins to take on anything non-infantry.
Riptide ACV Rush — This tactic involves building Riptides loaded with Javelin Soldiers. The Riptides transport the Javelins to the enemy while attacking enemy infantry at the same time, and the Javelins put a hole in the enemy vehicles and structures. This does not work against enemies with powerful base defenses.
Soviets
Flak Troopers and Bears — This tactic uses Flak Troopers and War Bears to quickly decimate an enemy base. The Flak Troopers use their Magnetic Mines on enemy structures and War Bears to ensure no infantry can bother you. If the enemy has managed to set up defenses however, your rush will probably fail.
Empire of the Rising Sun
Dojo Core Rush — A tried-and-tested strategy, the Dojo Core Rush involves rushing Dojo Cores to an enemy base and setting them up inside or nearby the base. Then you pump out Imperial Warriors and Tankbusters to quickly overwhelm and destroy the enemy infrastructure. While not foolproof, this tactic can destroy or severely cripple an unprepared enemy.
Defender-VX Rush - This is a strategy to quickly destroy the enemy base and their units. You send in lots of Defender-VX nanocores into the enemy base (or outside their base) and it will destroy most of their base. This strategy works well on soviet players because their structures slowly build up. But be warned this will only work on an unexpected opponent and may be destroyed before it is fully built.