Verbs (i.e, actions) can be very ambiguous, especially the common ones (to be, to do, etc.) and to parse a phrase you must first resolve this ambiguity using the context of that phrase. This context comes from many sources, including prior phrases and things like social and gestural cues, but mostly from the subject and object of that particular phrase.

I'm not sure how relatively important the subject is versus the object for resolving ambiguity, but I'm hypothesizing that by putting the subject as early as possible in a phrase, SOV and SVO languages take advantage of priming effects (see http://en.wikipedia.org/w/index.php?oldid=257117356) to speed the parsing of a sentence.

(Edit: As a side note, I'm curious about free word order languages such as Russian -- with what frequency and under what situations do they use the various word orders?)

Priming effects play a much smaller role in sentence comprehension than straight short term memory storage and retrieval. Speed influence is possible but priming effects act on different timescales than that of on-line processes used for comprehension.

Regarding your other response above, which I mostly agree with, there is a common conception among Japanese speakers that in English, since the action is mentioned halfway in the sentence, one can often predict the meaning of the sentence and effectively stop listening; in Japanese (or any SOV), one has to pay attention to the end otherwise they will have understood nothing.

This is somewhat true, in that you basically have to "suspend processing" until the verb appears, whereupon can you "fire" the processes. (The part that is mistaken by the Japanese is that when an English speaker figures out the rest of the sentence is because the object is inferred. But the same level of understanding is available.)