A nonaggression pact was an agreement between two or more governments to abstain from engaging in open warfare with each other. Nonaggression pacts may have lead to mutual cooperation in some matters and expanded trade, but were not as strong as formal alliances.
In 2368, Jean-Luc Picard proposed signing a nonaggression pact with the Tamarians, "possibly leading to a trade agreement and cultural interchange" but Dathon was unable to understand what he said. (TNG: "Darmok")
The Dominion signed nonaggression pacts with the Tholians, the Miradorn, the Romulan Star Empire and the Bajorans prior to the beginning of the Dominion War. Odo considered these to be impressive inroads into the Alpha Quadrant for the Dominion. (DS9: "Call to Arms")
The Bajoran nonaggression pact was a way the Dominion hoped would separate Bajor from the Federation. Weyoun came to Deep Space 9 in late 2373 to begin negotiations for the pact with Kai Winn Adami, but an agreement was not reached until sponsored by Emissary Benjamin Sisko as a method to prevent Bajor's ruin in the event of war between the Dominion and the Federation and its allies. (DS9: "In the Cards")
In 2374, Julian Bashir, Jack, Lauren, Patrick and Sarina Douglas predicted that if the Federation signed a peace treaty with the Dominion, the Romulans would vote to abandon the nonaggression pact with the Dominion at the upcoming plenary session. (DS9: "Statistical Probabilities")
The Romulan Star Empire did withdraw from their agreement, but sooner and much differently than Jack and the others had predicted. It was due to the death of Senator Vreenak, the man who negotiated the Romulan pact, after he was apparently assassinated by the Dominion. In fact, his ship had been destroyed by a bomb planted there by Elim Garak. (DS9: "In the Pale Moonlight")