State-run television showed footage of sparsely attended concerts and parades in cities across the vast country and there was much less fanfare over the event than in previous years.
President Vladimir Putin - who last year spent the anniversary visiting Crimea - was not expected to take part in any of the official celebrations that include a concert and firework display in Moscow.
Russia seized Crimea from Ukraine in 2014 following the ouster of its Kremlin-backed leader by mass protests in Kiev.
The Kremlin argued it was reacting to an illegal coup in Kiev. The move unleashed a wave of nationalist sentiment that saw Putin's popularity soar, with many Russians seeing the region that once belonged to Moscow as their country's rightful property.
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The annexation plunged ties between Russia and the West to their lowest level since the Cold War, as the US and EU responded with sanctions against Moscow.
"Three years ago Russia committed a crime many thought unimaginable for 21st century - occupied Crimea," Ukraine's foreign ministry wrote on Twitter.
Ukraine said today that four of its soldiers were killed along the volatile frontline in fighting over the past 24 hours.