Yes. There are several instances where he actually does and there is at least one time when he thinks it (Harry is Voldemort or senses his thoughts) he's close enough to where he can then Apparate.
The Order of the Phoenix
The duel with Dumbledore in the Ministry of Magic
Voldemort Apparates in the Ministry atrium. The following examples are from the chapter The Only One He Ever Feared:
At first Dumbledore created a flame that wrapped itself around Voldemort; but momentarily the rope because a serpent, released Voldemort who then Disapparated:
[...] Dumbledore had drawn back his and waved it as though brandishing a whip. A long thin flame flew from the tip; it wrapped itself around Voldemort, shield and all.
For a moment, it seemed Dumbledore had won, but then the fiery rope became a serpent, which relinquished its hold upon Voldemort at once and turned, hissing furiously, to face Dumbledore. Voldemort vanished. The snake reared from the floor, ready to strike — There was a burst of flame in midair above Dumbledore just as Voldemort reappeared, standing on the plinth in the middle of the pool where so recently the five statues had stood.
Voldemort also Disapparates just as the Aurors arrive (just after):
'Yes,' said Harry, shaking so violently he could not hold his head up properly. 'Yeah, I’m — where’s Voldemort, where — who are all these — what’s —'
The Atrium was full of people. The floor was reflecting emerald- green flames that had burst into life in all the fireplaces along one wall, and a stream of witches and wizards was emerging from them. As Dumbledore pulled him back to his feet, Harry saw the tiny gold statues of the house-elf and the goblin leading a stunned-looking Cornelius Fudge forward.
'He was there!' shouted a scarlet-robed man with a ponytail, who was pointing at a pile of golden rubble on the other side of the hall, where Bellatrix had lain trapped moments before. 'I saw him, Mr. Fudge, I swear, it was You-Know-Who, he grabbed a woman and Disapparated!'
Complementing the above: Dumbledore casts an anti-Disapparation spell to prevent the escape of Death Eaters before he duels Voldemort.
When Dumbledore arrives at the Ministry at the end of The Order of the Phoenix he casts an anti-Disapparation spell so that the Death Eaters could not Disapparate away. Only Bellatrix is saved because she was in the atrium and Voldemort took the time to rescue her (although the film portrays it as if she was gone during the battle in the book she was pinned magically by a statue by Dumbledore) as I cited above. He tells Fudge that there were Death Eaters in the Ministry after Voldemort Disapparates with Bellatrix just as Fudge and the Aurors arrive in the Ministry:
'If you proceed downstairs into the Department of Mysteries, Cornelius,' said Dumbledore, apparently satisfied that Harry was all right, and walking forward so that the newcomers realised he was there for the first time (a few of them raised their wands, others simply looked amazed; the statues of the elf and goblin applauded and Fudge jumped so much that his slipper-clad feet left the floor), 'you will find several escaped Death Eaters contained in the Death Chamber, bound by an Anti-Disapparation Jinx and awaiting your decision as to what to do with them.'
The Deathly Hallows
Voldemort also Apparates in The Deathly Hallows; Harry also reads his thoughts when he says to himself that he would soon be close enough to Apparate. The following examples are those I can think of off the top of my head:
The Battle of the Seven Potters
At the end of the Battle of the Seven Potters just after Voldemort's wand (which means Lucius' wand) was destroyed by Harry's wand he tells Selwyn to give him (Voldemort) his wand. However at this point Harry and Hagrid arrive at a safe house and Voldemort disappears. It's true he can make himself invisible but it's unlikely this is the case because he had no reason to stay there:
He felt Voldemort before he saw him. Looking sideways, he stared into the red eyes and was sure they would be the last thing he ever saw: Voldemort preparing to curse him once more — And then Voldemort vanished.
And indeed Voldemort did not return then; Harry was surprised at this:
He could not understand where Voldemort had gone and expected him to swoop out of the darkness at any moment.
But Voldemort did not swoop out of the darkness which means he indeed did Disapparate because he (Voldemort) knew it would be impossible to get through until the Ministry had fallen (but see below). Harry realises this shortly after:
Now Harry understood why Voldemort had vanished; it had been at the point when the motorbike crossed the barrier of the Order’s charms.
In addition though Harry reckons that Voldemort Apparated to the Death Eaters that recognised Harry:
Harry explained briefly how the Death Eaters pursuing them had seemed to recognise him as the true Harry, how they had abandoned the chase, how they must have summoned Voldemort, who had appeared just before he and Hagrid had reached the sanctuary of Tonks’s parents.
Whilst it's not clear if he did indeed Apparate I think it's quite probable he did esp because he knew he was short on time; after all Voldemort had already had a wand destroyed and certainly they would be at safe house soon.
The subject of the word 'vanish' versus 'Apparate' just after Harry and Hagrid reach the safe house
Alex suggested in the comments that the word vanish might not be indicative of Voldemort Apparating. This is admittedly something I thought of and I had similar reasoning: that Voldemort might well have tried to penetrate the defences even if only momentarily; he wasn't one to give up easily after all and he knew magic that nobody else did. It could be interpreted that reaching the safe house the two of them couldn't see each other due to the defences set up. But whether or not Voldemort Apparated at that moment what is certain is he would have Apparated once he realised he could not penetrate the defences. Of course Harry was also moved to the Burrow not long after that.
The beauty of the imagination is that you can interpret things in different ways from people reading the same thing but does it matter much if you look at it differently but enjoy it that way? I don't think so; that takes the magic away from reading and that's not something I would ever do deliberately. If you want to interpret 'vanish' as Apparate you can; if you don't want to that's also fine: Alex cited a quote that can also be interpreted different ways. In my mind when Harry imagines Voldemort it's not the same as when he is or feels Voldemort there.
Either way though Voldemort would have Apparated away once he found out he couldn't get through. Is there literal proof? Perhaps not but he wouldn't have wasted his time flying when he could Disapparate would he?
Voldemort also Apparates just as Harry and Hermione flee Godric's Hollow:
And then his scar burst open and he was Voldemort and he was running across the foetid bedroom, his long white hands clutching at the windowsill as he glimpsed the bald man and the little woman twist and vanish, and he screamed with rage, a scream that mingled with the girl’s, that echoed across the dark gardens over the church bells ringing in Christmas Day. . . .
And Harry thinks again on it two days later:
After two nights of little sleep, Harry’s senses seemed more alert than usual. Their escape from Godric’s Hollow had been so narrow that Voldemort seemed somehow closer than before, more threatening.
Harry is Voldemort as the trio are in Malfoy Manor; Voldemort had been summoned and this is what Harry witnesses:
Harry knew it; his scar was bursting with the pain of it, and he could feel Voldemort flying through the sky from far away, over a dark and stormy sea, and soon he would be close enough to Apparate to them, and Harry could see no way out.
I do not know if there are other examples but the above are quite a few instances where he does Apparate. It makes sense too doesn't it when you think about it? He was the most brilliant student Hogwarts had ever seen and there were numerous times Voldemort was called and he would want to get there as quickly as possible. The only way to do that would be to Apparate; that is to say the quickest way would be to Apparate. This includes at least once in battle with Dumbledore as I cited earlier.