For which peoples were bridges, ladders and tunnels important elements in their military successes?

I would say that ladders, bridges, and tunnels were most important for ancient people and their manner of fighting. If you read the battle descriptions of the Romans, you will immediately see that these things were absolutely important for warfare. For example, if you are going to besiege a city that is holding out, you would want to either have huge ladders or siege work that functions as ladders to scale walls, or build tunnels to get under the walls. These were the two ways to get into a walled city.Therefore see all of these things in Roman warfare.

Bridges are also very important, because military campaigns were very mobile and speed was something that was necessary. In fact, speed was one of the most important factors. Caesar, in his description of the Gallic wars, describes how he was able to build bridges over even fast moving rivers to shock his enemies. To make a long story short, bridges, tunnels and ladders were essential for warfare until the modern period or the invention of gunpowder.