Swiss pikemen were famous because with their discipline, they were able to both counter the heavy cavalry and move on the offensive. Thanks to their mercenary tradition, they were well-drilled, disciplined, fearless, and for the most parts quite loyal.

They proved their mettle in the battles of Grandson and Murten where they beat the Burgundians through aggressive movements. Not only were they fearsome when winning, they were also impressive in defeat. At Marignano, their disciplined retreat enabled them to maintain strategic power. So much so that France entered into "Eternal Peace" with the Swiss following that battle, with King Francis I himself declaring, "I have defeated those that only Caesar has defeated."

But their military prowess was not the only factor. Their tradition of campaigning each year means they could be reliable partners, and they became important parts of French armies in the Italian wars. Swiss communities included military training in their tradition, so they had a reliable supply of trained troops.

The Spanish commander Gonzalo Fernandez de Cordoba eventually invented a new fighting system based on the tercio where close-order coordination between firearms and pikes could beat the pike-heavy Swiss formations. Over time, the Spanish were able to win the Italian wars, including the ignoble defeat and capture of Francis I in the 1525 Battle of Pavia.

Source: Fighting Techniques of the Early Modern World by Jorgensen, Pavkovic, et al.