What are the different traditions/contribution brought by the romans?

In addition to the points listed by chief66, there are:

a) language--almost all of French, Italian, Spanish and Portuguese (the Romance languages) and a substantial portion of English is descended from classical Latin

b) military expertise and the ability to run a military dictatorship-the Roman legions were brutal but extremely effective

c) the Romans transmitted Greek learning, philosophy and art. Although the Roman attempts to duplicate (or improve) the Greek legacy often fell short of the original, what they did pass on was a huge gift to the world

d) Not a benefit: a numerical system that might have been effective when it was first started, but could not handle computations or large numbers. It strangled commerce and science well into the Common Era.

Well most of traditional Europe has Rome to thank. When Christianity became the dominant religion and the others were hunted down and persecuted the former pagan holidays became the Western Worlds holidays. The days like Christmas and Easter were originally Roman holidays, but were subverted by the Christian church.

Other inventions such as the aqueduct and plumbing were a Roman development, quality roads, organized volunteer militarys, plenty of construction techniques, well crafted Iron products, and medicine all can be attributed Rome (although some were from some areas which Rome came to encompass at one point or another). It is strange how so many of those developments were lost in the Dark Ages, after all, modern medicine did not catch up to Roman abilities until the period between the Crimean and First World War!