Do both countries have a particluar hot spot that existed in the past, and if so, does it still exist now? Have their wars historically been bloody or transient, and are they now considered "friends"?
Rather than saying they had X number of wars, it would probably be more accurate to say that the two countries had a continuous ongoing conflict from 1895 until 1947, with occassional brief breaks for recuperation and retooling. In fact, the territorial disputes didn't even really end there, but the fighting did due to the Cold War.
Since then I think just about all the disputes have been resolved, save for the status of four small islands near Sakhalin.
Russia and Japan had one war, and several smaller scale conflicts, in the 50 years between 1895-1945. They are NOT natural enemies.
Their emnity arose out of the power vacuum created by the collapse of China in the lat 19th, early 20th century. This caused them to both covet Manchuria, for two different reasons.
Russia wanted a warm water port on the Pacific. Port Arthur (in Manchuria, leased from China) served the purpose. Vladivostok (ice-bound for four months of the year), did not. Japan wanted the Manchurian INLAND for its natural resources and living space. That was the cause of the 1904-05 war.
China has since "woken up" and re-asserted her claim to Manchuria, thereby removing the main source of emnity between Russia and Japan.
It is noteworthy that although there were two "border incidents" before World War II, Russia and Japan had, and observed a non-aggression pact for most of the war (until Germany was defeated). Essentially, they both had "other fish to fry."
I wouldn't call Kuril islands "four small islands near Sakhalin". They indeed do belong (administratively) to Sakhalin region (oblast) of Russia -- but they are about ten times closer to Hokkaido than to Sakhalin.
Anyways, there were as we all know, two main conflicts - Russo-Japanese war of 1904-05 and Soviet-Japanese war as part of WWII in 1945.
Then there was a Khalkhin-Gol conflict in 1939 - which was not an officially declared war, but a rather major conflict anyway which lasted for about four months and had around 50,000 losses/casualties.
I would call that a war deserving to be counted here - it had about as many human losses as WWII Soviet-Japanese war (although K-H conflict's importance was certainly lower). It also lasted longer than the latter.
As for Khvostov-Davydov episode, it was a cruel (and stupid) attack but to call it a war would be kind of strange. Then you'd need to call a war every incident when a band of guys with some weapons from country A invades a tiny village in country B, destroys homes and kills people then goes back without doing much else.
Those two officers, formally, were not authorized by the Russian government to conduct any raids. However, the whole incident looked very strange - they were put in jail, then sent back to Russia to fight in Russo-Swedish war in 1806 and when they came back to St.Petersburg they both (!!) fall from a bridge and drown (two experienced sailors on a warm summer night!!). Bodies were never found. Quite suspicious and mysterious, to say the least.
One of the theories says that they were attempting (under orders from their commanding officer, Nikolay Rezanov) almost exactly the same that commander Matthew Perry only threatened Japan with about 50 years later when US decided to "open up" Japanese empire. Seems kind of weak theory to me, but it is still possible that Rezanov simply did not understand local culture, politics etc, so out of desperation... or perhaps he was that kind of guy... he just went with brute force approach.
on Khvostov-Davydov affair
Давыдов Гаврил Иванович. Двукратное путешествие в Америку морских офицеров Хвостова и Давыдова, писанное сим последним: Часть 1, Морская типография, СПб, 1810 (333 с.) (In Russian; Davydov's unfinished autobiography, part 1)
Русский биографический словарь в 25 томах. — СПб.—М., 1896—1918. (in Russian: Russian Biographic Dictionary in 25 Volumes)
on Rezanov and his Japan mission
Anton Chekhov, Остров Сахалин (in Russian, 1893-95); The Island. Journey to Sakhalin (in English, Washingtson Square Press, 1967)
Owen Matthews, Glorious Misadventures. Nikolai Rezanov and the Dream of a Russian America, Bloomsbury, 2013.
In 1806 and 1807, Russian naval officers Khvostov and Davydov destroyed about four Japanese villages at on Sakhalin and the Kuriles (details are in Richard Pierce's "Russian America: A Biographical Dictionary"). Apparently the Japanese government did not retaliate, but I consider those attacks to be war.