In the BBC radio 4 series The Wild East, the history of Russia after the Mongolian occupation is described as if all the bad things happend subsequently had been caused by the legacy of that era. Isn't there any positive legacy of the Mongolian occupation in Russia ? For example, didn't the newly opened up trade route to the east benefit the economy of Russia ? Wasn't the cultural influence from the east one of the appeals of the Russian music to the West European audiences in the early 20th century ?
Interesting question and highly creative conjectures but ultimately the answer is no. The trade routes didn't play much of a role: Russian trade remained oriented on Western Europe; as for the great Russian music, it was the product of the 19-20th centuries and followed and developed, once again, Western patterns.
So, to sum up: I can't think of any positive influence the Mongol overlordship had (it's a more accurate term then occupation, in this context). The negative legacies are legion.
EDIT: I was asked to provide references. Right now on the fly I found this chapter (in Russian) from a recent (2001) book called "Ten centuries of Russian mentality". I'll quote a bit in the original:
Татарское владычество наложило свою печать на характер русских князей: сознание постоянной опасности довело до высшей степени свойственные им недоверчивость и осторожность. Резко изменился и образ их жизни. С появлением татар князья и их окружение стали запирать своих жен в теремах, прятать свои сокровища в церквах и монастырях. Н. Карамзин писал об этом периоде: «Забыв гордость народную, мы выучились низким хитростям рабства, заменяющим силу в слабых; обманывая татар, более обманывали и друг друга; откупаясь деньгами от насилия варваров, стали корыстолюбивее и бесчувственнее к обидам, к стыду, подверженные наглостям иноплеменных тиранов. От времен Василия Ярославича до Иоанна Калиты (период самый несчастнейший!) Отечество наше походило более на темный лес, нежели на государство: сила казалась правом; кто мог, грабил; не только чужие, но и свои; не было безопасности ни в пути, ни дома; татьбы сделались общею язвою собственности»13. Ему вторил А. Герцен, писавший позднее: «У преследуемого, разоренного, всегда запуганного народа появились черты хитрости и угодливости, присущие всем угнетенным: общество пало духом » 14.
For lack of time I'll have to make do with a slightly-edited Google Translate translation:
Tatar domination has left its mark on the character of the Russian princes: consciousness constant danger brought to the highest degree the inherent distrust and caution. Dramatically changed their way of life. With the Tatar princes and their entourage were locked in a mansion of their wives, hide their treasures in churches and monasteries. Karamzin wrote about this period: "Forgetting the people's pride, we learned the low cunning of slavery, which substitutes for force in the weak, deceiving the Tatars, a cheat, and each other, buying off the the violence of the barbarians, became greedy and insensitive to insults and the shame, exposed to the rapacity of foreign tyrants. From the time of Basil Yaroslavich until John Kalita (during the most miserable!) our motherland was more like a dark forest, rather than a state: might was right, and who could, robbed, not only strangers, but also his own people, there was no security neither on road nor in home; seizure of property became a common plague" He was seconded by Alexander Herzen, who wrote later: "The persecuted, ruined, always frightened people acquire the features of cunning and obsequiousness, common to all the oppressed: the society has fallen in spirit".
I would recommend reading Lev Gumilëv works if you'd like to look onto positive sides of Mongol (or Tartar-Mongol) occupation, starting with this assay (1)[in Russian] and its main source (2). One of his points is that Mongols were allies in fight against Teuton and Livonian orders.
As to neutral impact, one should first of all look at the numerous loanwords from Turkic languages, such as e.g. 'Kreml'
1) Луков Д. Особенности позиции Л.Н. Гумилева по проблеме Русь и татаро-монголы. Томский Политехнический Университет
2) Гумилёв Л.Н. От Руси к России. - М.: Прогресс.
Also Karamzin, who was mentioned above, is of Turkic origin (name coming from Turkic 'Kara Murza', Black Prince).
The biggest positive effect that the Mongols had was the unification of Russia into a more or less centralised state under a single ruler. Russia had long been divided in city-states with varying degrees of political association and cooperation. The Mongols broke the power of most of these city-states. With the big powers such as Kiev and Vladimir taken out, smaller cities such as Moscow managed to prosper.
The city of Vladimir never recovered as well as Moscow did from the blow it had been dealt, and eventually it was eclipsed by Moscow in importance. Especially when Moscow became the religious capital of Russia. Vladimir had been the seat of the metropolitan of Kiev (the religious leader of Kievan Rus'), but in 1325 this seat was moved to Moscow.
Moscow prospered even more after the khan started to directly support its domination of Russian lands in an effort to counter the rising power and influence of Lithuania. Eventually Moscow grew powerful enough to defeat the Mongols and unite most of the cities of Russia in a single state. That is probably the only real positive effect the Mongols had on Russia.
my guess is that cultural transfer from mongols to russians was huge.
no that they teach russians to build ships, calculate trade and play flute, but consider this:
sophisticated 'honour' system between lords distinguish russian from european mentality until now. and allow russians to survive many turbulent periods. mongol operation of masses and armies was more eye-eye, body-body contact and feeling to feeling, rather than western word-by-word, paper-by-paper approach. and russians seem learned that from mongols to my vision. russians will follow the leader that will breathe and blink at a proper rate rather than the one who speaks right words about freedom.
even these days this approach allows putin to consolidate forces around kremlin. this is definetly positive if existance of russia is considered positive.
then russians learned about asia from mongols, which later allowed to extend small country to the pacific, to persia and to china borders. is that positive?
yes the idea that russia those days was not occupied but rather like a state within US is accepted by many russians. then invasions should be called local suppression.
above someone mention religion-tolerance. yes, seems to me, russian culture in this area is also seem to be mongol-like. russian will not follow religious rituals in detail but would try to achieve God's(or ancestor or spirit) support in their activites. Russians for centuries would base their strategic decisions on their religion experience. Last czar planned WW1 activities based on "advices from god" he received while praying or from prophets (like rasputin).
just like mongols russians will support or leave alone those who pray the 'right god', and cast away or kill those who pray to a 'wrong gods'. this is quite positive, in some sense. as western style of religion-tolerance is to leave alone anybody who claims to do praying.
of course mongol unwritten 'honor system' or 'the way to communicate and cooperate efficiently in sophisticated manner across large areas in long term over generations without breaking apart in small fractions' is what holds russia together until now. this is most positive outcome. I cannot see how russia would survive so close to burning europe without that "we are huge together" mentality of mongols.