We all know what Harry saw in the Mirror of Erised, he saw his family. We also know that Ron saw himself as Quidditch captain, Head Boy etc... But what did Dumbledore see? He claims he sees himself holding thick woolen socks:

~Quote~

Harry stood up.
"Sir - Professor Dumbledore? Can I ask you something?"
"Obviously, you've just done so," Dumbledore smiled. "You may ask me one more thing, however."
"What do you see when you look in the mirror?"
"I? I see myself holding a pair of thick, woollen socks."
Harry stared.
"One can never have enough socks," said Dumbledore. "Another Christmas has come and gone and I didn't get a single pair. People will insist on giving me books."
It was only when he was back in bed that it struck Harry that Dumbledore might not have been entirely truthful. But then, he thought, as he shoved Scabbers off his pillow, it had been quite a personal question.

~End of Quote~ (pg 157 Philosopher's Stone)

Harry is of course right, it is a very personal question. I think it's very unlikely that Dumbledore saw himself holding socks, so what did he really see? Did he have a particular reason for not telling Harry the truth? *mystery*
I think it might have been something to do with Harry falling in love (love to defeat Voldemort.) So DD might not have told Harry what he saw because Harry wasn't ready to know about the prophecy. On the other hand Dumbledore is slightly loopy! But what do you random peeps think?