In The Godfather I, when Michael Corleone took refuge in Sicilly, he met Apollonia and then met the inn owner who happened to be Apollonia's father. Michael wanted Apollonia to be his wife and he talked to her father about it. But before he started talking, he asked one of his bodyguards to translate what he was going to say in English into Italian (at about 1h 41min). I just don't understand why. I'm sure that Michael was able to speak Italian-- when he met Sollozzo and that cop he was surely able to talk with Sollozzo in Italian. So why would he speak English and need a translator rather than speak Italian this time?
Michael Corleone was born in America. Since his early age he stayed away from family business, so he didn't have that typical Italian family essence, so it was obvious that he didn't have fluent dialect when it comes to speaking in Italian Language. On top of that talking in Sicilian dialect is even tougher.
Another thing is that he was an outsider for them, he wanted to show Apollonia's father that he comes from a family with power so that he would consider him for his daughter. If he would have spoken himself, chances are that Apollonia's father would not have believed him, plus not talking to her father directly gave an indication that he's not too desperate (though he was) for her and not talking directly gave an indication that he belongs to a family of means.
Another thing is that he wanted to show respect and do it the Sicilian way. This gave another indication to his father that though he is not from Sicily he has not forgotten his Sicilian roots.
When he met Sollozzo, it was Sollozzo who said, Mike and I are going to speak Italian (and I believe they might have been speaking Sicilian). Two points:
If they were speaking Italian and not Sicilian, then Mike would have maybe not even understood Sicilian although since his dad was Sicilian, why not?
But the big thing was, The Turk wanted to speak Italian and while Mike understood it (if he did; he really could not have cared too much what was being said) he at one point felt the need to express himself in English -- his Italian and/or Sicilian was not fluent.
I agree it seemed like Michael could understand fluent Italian but couldn't speak it as well though that said he was able to speak it better in "The Godfather 2" and 3.
Also, I agree with Jeff's answer but I feel to a degree, he wanted to say what he wanted in English as to get the point across to not only Sollozo but also to Captain McCluskey as well. He wanted them both to know that he wanted his father left alone from that point onwards.
To the excellent answers already here, I would add this one additional point:
It is very important to Michael, at that moment, that he not give Apollonia's father offense. If he spoke for himself, he might make a grammatical or pronunciation error that made the conversation go awry. If you note what he has his bodyguard say, he takes great care to be as respectful, courteous, and formal as possible.
Given what we know of his level of Italian fluency, he could probably have managed it himself. He just didn't want to risk it.