At many points in the story, when Dumbledore asks Harry something, he gives him a piercing look. It makes me wonder if that is Dumbledore using Legilemency against him. Is he?
He certainly seems to find some information when giving Harry these 'piercing looks', but he still doesn't know about harry hearing the basilisk in the Chamber of Secrets, so I would say no; he's just extremely smart, so he makes some educated guesses as to what Harry is thinking.
I would also say that Dumbledore would feel it is rude to intrude on Harry's thoughts with legilimency, which is likely the reason he gives Harry plenty of opportunity to tell him his thoughts of his own accord. Harry's free will would factor greatly into Dumbledore's decisions.