As an example, Back To The Future III on USA has “He’s as asshole!” dubbed to “He’s an idiot!”.
So, do they pay the actor to dub his own voice for a gazillion dollars, or get someone who sounds like him?
It depends on a variety of factors.
A large part of most Hollywood movies are dubbed. Look at a scene where someone’s walking through a crowded room, or down a street. Don’t look at the characters, but at the stuff going on in the back ground. Listen to the audio track. Notice that you can’t hear a hint of most of it. So it’s obviously no problem to have the actor dub something else than what they orginally said – they were going to dub it anyhow.
There’s an example of this in “North-by-Northwest”, Eva Marie Saint, meeting Cary Grant on the train actually something to the effect of “I never make love on an empty stomach”. It’s dubbed out.
In “My Fair Lady” Audrey Hepburn’s songs are mostly dubbed by Marnie Nixon (Audrey couldn’t sing – for this they gave up Julie Andrews??)
In “Das Boot” the German lead dubbed the English version, because he happened to speak both. Other voices were not the German actors.
TV versions are usually done by the actual actors, yes. There are exceptions when they’ll get a sound alike (if, for example, the actor just isn’t available and they have to deliver), but it’s almost always the actor. They just pick up the TV-safe lines when they’re in the studio looping lines for the actual theatrical-release of the film. It’s a standard part of an actors contract, several days of looping, so they don’t have to pay them anything beyond what they would have had to have paid them anyway.
Thanks, Ana.
There’s another option, though it’s less common. Occasionally, when a scene is shot, another version of the scene will be shot in another take, usually with less profanity or nudity (wrap a towel around a woman in the bathroom scene, for example). This is known as the “airline version.”
And regarding looping, it’s worth knowing that in big Hollywood productions, perhaps less than five percent of what you hear in the finished film was actually recorded during the actual shoot. Obviously, the music score was added later. Ditto for special sound effects, like gunshots and car crashes. Ditto for not-so-obvious sounds, like footsteps and doorknobs. And ditto for dialogue, though how much is redone varies from movie to movie.
And most oddly, crowd scenes are almost invariably shot silent, with the exception of the lead actors. That means the crowd is jumping up and down, or running around, or whatever, in mime. This is done so the lead actors can be recorded cleanly, allowing the crowd noise to be added seamlessly after the fact without creating big ugly jumps in sound on the edits.
Likewise, in-scene music (like at a concert or nightclub) is also added later. The crowd dances to nothing, or at best a guy on a ladder setting a rhythm by waving a stick so they’re all in sync. When you know this, you can suddenly be annoyed to notice that the lead actors are talking in normal voices, and the music is turned down faintly in the background, whereas in real life the sound in the club would be so loud you’d have to shout. Inexperienced directors will forget to have their actors yell at each other, pretending there’s loud noises going on, so it matches later when the music is added. The first few seasons of “Buffy the Vampire Slayer,” for example, are really bad at this when they go into the Bronze; based on the volume of conversation in the foreground, you’d think the band on stage was playing on “mute” mode.
Not directly germane to the original question, perhaps, but it serves as additional background for understanding just how fake the soundtrack of a finished film really is.
Cervaise’s five percent figure sounds about right, except for dialogue. Looping onscreen dialogue is pretty tedious and time-consuming. On set, you keep everything else as quiet as possible to get as much of the dialogue clean as possible. If you’re using less than five percent of your set dialogue, it’s time to find a new sound mixer. And you’ve got a very angry producer. 
Couldn’t agree more about the fakeness of club scenes. My film took place in and around a noisy nightclub, and we worked out a number system for how loud the actors should talk/yell, depending upon where they were in the club. Smack in the middle of the dance floor was a 10; yelling. At the bar on the outskirts of the club, while in real life probably would have been almost as loud as the dance floor, was a level 5 for film purposes, or talking louder than normal. And the hallway just off the main dancefloor, behind a closed door, was a 1, or just a little bit louder than normal conversation. Anywhere else was normal conversation level. It was a little weird for some of the actors at first, because they were yelling to be ‘heard above the crowd’, but as Cervaise points out, it was actually just a quiet room.
And we dealt with the dancers keeping time this way: before camera rolled, we’d have twenty seconds or so of music playback, so the dancing extras could keep the beat. We’d kill the music, and camera would roll, and the dancers could keep going at the right pace. We had no way of knowing what our final music would be, of course, but we knew the approximate beats per second we wanted it to be.
Okay, that had almost nothing to do with the OP. But it’s still an interesting subject. 
partly, as much as I like Julie Andrews, Audrey Hepburn was much better for the part of Eliza. Played Freddy once myself, so I should know.
All of Hepburn’s singing was dubbed, but it’s hardly true that she cannot sing. She’s a perfectly adequate singer as evidenced by the original track for “Wouldn’t It Be Loverly” on the My Fair Lady dvd, and that’s her doing a respectable job in Funny Face. But because she was a woman, adequate wasn’t good enough.
It was routine at the time for women in musicals to be dubbed by professional singers if they were not considered good enough singers. Marti Nixon was an old pro by the time she did My Fair Lady, having dubbed Natalie Wood in West Side Story and Deborah Kerr in The King and I.
I say women particularly because the men were nearly always permitted to do their own singing, even those, such as Marlon Brando, Clint Eastwood, and Lee Marvin, who are truly awful singers.
It’s more a product of sexism–the women’s parts had to be flawless, while the men’s could be flawed if the actor were a big enough name–than it is a product of Ms. Hepburn’s singing ability.
You see the same thing in modern Hong Kong action movies. The top male stars usually are martial artists who’ve been taught to act, while the female stars are actress and models who’ve been taught martial arts.
Besides which, had Julie Andrews played Eliza, she would have been unavailable to play Mary Poppins, which shot at the same time, and that would have been a shame.
Audrey Hepburn did most of her own singing for the number “Just You Wait” in My Fair Lady, with a few bars of Marni Nixon interpolated here and there. Probably because it was a comic song more than it was melodic.
She also sang the Oscar-winning “Moon River” on her own in Breakfast at Tiffany’s. Henry Mancini wrote it for her range.
Clearly whether one prefers Audrey’s, Julie’s or Marnie’s voice is largely a matter of taste. As I recall, tho, Audrey’s original singing was on an alternate track of the “My Fair Lady” DVD; again, if memory serves, it was quite weak.
I’m curious “I am Sparticus” why you think Julie Andrews couldn’t have been Elisa – she had been playing it on Broadway for years, hadn’t she?
If Julie Andrews had missed “Mary Poppins” that would have been sad, indeed.