Obviously there are the Valyrian steel swords, but what other influences were there from the Empire prior to the eruption of the Fourteen Flames?
For some reason, the Valyrians never expanded the political and military reach to the Westeros mainland despite building an outpost on the island of Dragonstone.
However, that is not to say that the Valyrian Freehold did not have a substantial influence on Westerosi history.
The influence I am referring to are two mass migrations that were caused by Valyrian expansion. The first the Andal migration/invasion that resulted in the majority of Westeros (save the North), either submitting or assimilating with these foreigners. See Maester Yandel's World of Ice and Fire for more detail concerning the wars of the Andal Invasion and the impact the conquest and assimilation had on Westeros.
The second migration is that of the Rhoynar. After fighting a war against the Valyrians that resulted in millions of deaths and the destruction of their city-states during the Rhoynish Wars, warrior-queen Nymeria led thousands of refugees and fled Essos in ten thousand ships (Beldecar, in his History of the Rhoynish Wars, calls this an exaggeration). After years of struggle and journeying, Nymeria leads her people to Dorne. She allies with and marries Mors Martell, and it is through this alliance that Dorne is consolidated into a single kingdom ruled by House Martell.