History can have subtle but strong effects on the game. Especially when it comes to resources available for your fortress through trade. For example, if the dwarves did poorly throughout history, you may find that your home civilization is very small, and has a limited set of resources to provide. Certain critical items like bauxite, flux, or coal could be completely unavailable outside of whatever you have at your fortress. A successful civ during world gen will have a much larger territory and therefore a wider range of goods.
Since you play on smaller maps, you can often get situations where certain races aren't available at all. Lack of goblins makes for a quiet, uneventful fort. If the humans didn't make it, you lose out on their trade caravans. Lack of elves rarely bothers most players, but can still have an impact. Especially on a treeless map.
In addition, there is always the possibility that your civ will be at war with the humans or elves, which means they'll be hostile and come siege you. It can be exciting, but it also changes the game quite a bit.
It has an even stronger effect on Adventurer mode, since it dictates what you'll see and what will be around for you to fight.
All of this is even more profound if you use mods that add in more races, since there is even more activity going on during world gen.