Romans vs Samurai

Depends on the era the Roman Legion and the Samurai army comes from.  Roman armies could range anywhere from about 509 BC during the birth of the Republic to 1453 AD during the fall of Constantinople.  Samurai have a similar problem, spanning from the 12th century Gempei War to their 1873 dissolution with the Meiji Reforms.  Do the Romans have access to auxilia?  What auxilia?  Do the samurai have ashigaru? 

Let's say for this case that the Romans use a late Republican/early Imperial legions with auxilia while the Japanese use a similarly sized Sengoku period army (without firearms) comprised of many samurai and a main bulk of ashigaru.  The battlefield is clear with a plain field with minimal hills. Judging from the pictures, this should be appropriate (though the Romans during this time probably used chain mail).

In the infantry battle, the legion would probably prevail but with significant losses.  Legionary pila would be devastating in the opening stages of a battle and the samurai would probably not be able to hold against the Roman's disciplined CQC from the front for too long.  However, it is important to note that during Sengoku Jidai, Japanese armies focused on drilled ashigaru yari pike walls not unlike the phalangites of the Macedonians and Diadochi.  While I don't believe that the ashigaru would be enough to trounce the legion, I think that they could effectively pin and hold them off in the center allowing for the more heavily armed samurai to take advantage of any openings or flanks.

In range, the Japanese have a slight overall advantage due to their love of longbows both on foot and on horse.  This generally surpasses Roman slingers and bowmen (though composite bow armed auxilia might do okay).  Romans have superior siege weapons like scorpions, but with this army there probably wouldn't be a significant enough amount to overturn the samurai archers.

The cavalry battle really depends on the composition of the Roman auxilia since Roman cavalry at this time period sucked.  Samurai field superior horse archers and light/medium cavalry.  The samurai wouldn't have charging heavy lancers like they do in mainland Asia and Europe, but this wouldn't really be much of a disadvantage against the stirrup-less Romans and most of their auxiliaries.

Overall verdict: pyrrhic victory for the samurai.  The Sengoku army wins both the cavalry battle and the ranged skirmish which is necessary to defeat the slowly prevailing legions in the center.  With the barrage of missile fire and danger of encirclement by the samurai cavalry, the Romans would probably be forced to retreat.