Quite possibly. I don't think we can say definitively. But Dumbledore's character and beliefs can give us a good idea. Let's take the curses one at a time.
The Imperius Curse
I highly doubt that Dumbledore ever performed this. It seems to me to be an anathema to everything he stands for. Dumbledore, after all, was a profound believer in the importance of free will in individuals.
"It is our choices, Harry, that show what we truly are, far more than our abilities."
(Chamber of Secrets, Chapter 18, Dobby's Reward).
This is why he kept so much faith in people like Snape and Hagrid, people that others regarded as irreparable or untrustworthy. Dumbledore's belief in free choice meant that he looked past their former mistakes to see their future potential. Kidnapping someone, taking away their free will and forcing them to obey your every move is completely out of keeping with that philosophy. I think we can form an argument from silence here. If Dumbledore performed the Imperius Curse or approved of its use then I think we would have seen the Order utilising it. I'm not aware of that ever happening so I think we can conclude that Dumbledore didn't permit it.
The Cruciatus Curse
Perhaps Dumbledore used this. I doubt it.
The only hint I can find is in this exchange.
"You do not seek to kill me, Dumbledore?" called Voldemort, his scarlet eyes narrowed over the top of the shield. "Above such brutality, are you?"
"We both know that there are other ways of destroying a man, Tom," Dumbledore said calmly, continuing to walk towards Voldemort as though he had not a fear in the world, as though nothing had happened to interrupt his stroll up the hall. "Merely taking your life would not satisfy me, I admit-"
"There is nothing worse than death, Dumbledore!" snarled Voldemort.
"You are quite wrong," said Dumbledore...
(Order of the Phoenix, Chapter 36, The Only One He Ever Feared).
Perhaps this is an indication that Dumbledore would be prepared to use the Cruciatus Curse as an alternative way of "destroying a man". It certainly isn't a canonised use, though. Indeed, it seems likely from Dumbledore's tone that he's saying that there are ways of destroying someone without using Dark Magic whatsoever. Judging from how Dumbledore treated his other main nemesis (Grindelwald) he would probably imprison Voldemort if given the chance. Prolonged imprisonment with nothing but your own thoughts for company and the opportunity to mull on your past actions is a torture of itself. It seemed to induce some penitence in Grindelwald, anyway.
"They say he showed remorse in later years, alone in his cell at Nurmengard. I hope that it is true. I would like to think he did feel the horror and shame of what he had done."
(Deathly Hallows, Chapter 35, King's Cross).
All in all, I think it's highly unlikely that Dumbledore ever used the Cruciatus Curse. As a legendary Legilimens he could use Legilimency if he wanted to tease a secret out of someone. The passage above is the only one that hints that he'd be prepared to use it but I think we can rule it out.
The Killing Curse
This one is the most open to interpretation. All things considered, I think it's pretty likely that Dumbledore used the Killing Curse. We never see him do it, though. The reason I think it's likely is because of the general climate of the two wizarding wars. Duelling to kill was the norm.
"But if any of you attempt to sabotage our resistance, or take up arms against us within the castle, then, Horace, we duel to kill."
(Deathly Hallows, Chapter 30, The Sacking of Severus Snape).
"Harry, the time for Disarming is past! These people are trying to capture and kill you! At least Stun if you aren't prepared to kill!"
(Deathly Hallows, Chapter 5, Fallen Warrior).
"Crouch fought violence with violence, and authorised the use of Unforgivable Curses against suspects."
(Goblet of Fire, Chapter 27, Padfoot Returns).
So, whilst we don't have a clear-cut example of Dumbledore actually killing someone, it would've been odd if he didn't kill anyone during either of the two wars. As @MermishEssence says, he almost confirms as much to Harry.
"You never killed anyone if you could avoid it!"
"True, true," said Dumbledore...
(Deathly Hallows, Chapter 35, King's Cross).
This would seem to me to be a tacit confirmation from Dumbledore that he did kill, but only when the circumstances demanded it. If he'd never used the killing curse then it would've been reasonable for him to have replied to Harry like this: "True, indeed I never killed at all". War is a dirty business and as the leader of the Order of the Phoenix I think a circumstance where Avada Kedavra was necessary would've presented itself at some point. If he'd never killed then Dumbledore would have said as much. This is as close to proof as we can get. We do have instances of him Disarming or Stunning opponents when he could have killed them. I've already mentioned Grindelwald and his exchange with Voldemort in the Ministry. There's also these examples:
"If you proceed downstairs to the Department of Mysteries, Cornelius," said Dumbledore..."you will find several escaped Death Eaters contained in the Death Chamber, bound by an Anti-Disapparition Jinx and awaiting your decision as to what to do with them.
(Order of the Phoenix, Chapter 36, The Only One He Ever Feared).
"Don't kill me!" [Snape]
"That was not my intent." [Dumbledore]
(Deathly Hallows, Chapter 33, The Prince's Tale).
"He set Dawlish to tail me. It wasn't kind. I have already been forced to jinx Dawlish once. I did so again with the greatest regret."
(Half-Blood Prince, Chapter 17, A Sluggish Memory).
In conclusion, we don't see Dumbledore perform an Unforgivable in canon. He probably never performed the Imperius or Cruciatus Curses. He probably did kill at least once, but only when he had no other alternative.