There would be major differences both technologically and culturally.
Starting with technology, think back to all the basic tools that pretty much rely on the ability to grip - stone knives & spears, even into the future, ropes, pens, screwdrivers, swords, bows, even guns would be affected. I'm not saying they'd be impossible to use without opposable thumbs but certainly a lot more difficult and so probably wouldn't have developed as naturally as they did, if at all (difficult to use would mean thrown aside and forgotten).
I would wonder if we would ever get past the iron age, and would certainly be a lot slower to reach it and to advance beyond.
But why would that affect culture? Well presumably without such technology, the spread of mankind would surely have been much different. For a start, we would be less inclined to stand upright as user6760 said above. But even looking to more recent times, without the Long-bow would Britain have conquered as much as they did in the middle ages? Without such a mastery of ropes and knotting they would surely not have the dominant Navy they did, if indeed such a Navy could even exist. It's doubtful the Renaissance could have happened without the existence and skill in delicate instrumentation.
To build your world, if you were to be honest in your story, you'd need to start at the beginning of civilisation at the Stone-Age and imagine how each invention would be different if it was made for someone with no thumbs, and then the following generations of inventions would have to evolve from those, rather than from real inventions. You should find that quite quickly you have branched quite far away from what happened in real life.