Literal varian - Кто высоко летает, тот низко падает.
But there is much more expressive modern variant:
Быстро едешь, тихо понесут. (If you ride fast you will be carried slowly [in the funeral train]).
I meant it as a linguistic comment though ;-) : I meant that we seem to use the second part more often than the first. The fall is predicted or ascertained for lots of people having too much ambition, trying too hard, etc.
But that reminds: "Na hoogmoed komt de val" ! I.e.: after pride, hubris (too high a courage/ a feeling, let's say) there's the fall.
"Joka kuuseen kurkottaa, se katajaan kapsahtaa."
Literal translation: "Who reaches for the spruce, falls down onto the juniper."
Translation: "If you reach for something that is far too good for you, it is not going to end well."
The English transliteration is "koito leti/hvarchi visoko, nisko pada". The literal meaning and the idea of the phrase is the same as in Slovenian, Croatian and other Slavic languages (see above) - the meaning is roughly "who thinks too/extremely highly of himself (implied by "flying high"), ends badly (implied by "falling low")."