first thing that popped into my head when i think of a great phone conversation in a movie:

http://www.youtube.com/watch?v=yT2cJg8lut8

rewatching it, while the phone doesn't get much screen time i still think it's one of the creepiest, most inventive uses of a phone

DR STRANGELOVE- President On The Phone.

http://www.youtube.com/watch?v=hWP_rEWG2xk

President Merkin Muffley: Hello?... Uh... Hello D- uh hello Dmitri? Listen uh uh I can't hear too well. Do you suppose you could turn the music down just a little?... Oh-ho, that's much better... yeah... huh... yes... Fine, I can hear you now, Dmitri... Clear and plain and coming through fine... I'm coming through fine, too, eh?... Good, then... well, then, as you say, we're both coming through fine... Good... Well, it's good that you're fine and... and I'm fine... I agree with you, it's great to be fine... a-ha-ha-ha-ha... Now then, Dmitri, you know how we've always talked about the possibility of something going wrong with the Bomb... The *Bomb*, Dmitri... The *hydrogen* bomb!... Well now, what happened is... ahm... one of our base commanders, he had a sort of... well, he went a little funny in the head... you know... just a little... funny. And, ah... he went and did a silly thing... Well, I'll tell you what he did. He ordered his planes... to attack your country... Ah... Well, let me finish, Dmitri... Let me finish, Dmitri... Well listen, how do you think I feel about it?... Can you *imagine* how I feel about it, Dmitri?... Why do you think I'm calling you? Just to say hello?... *Of course* I like to speak to you!... *Of course* I like to say hello!... Not now, but anytime, Dmitri. I'm just calling up to tell you something terrible has happened... It's a *friendly* call. Of course it's a friendly call... Listen, if it wasn't friendly... you probably wouldn't have even got it... They will *not* reach their targets for at least another hour... I am... I am positive, Dmitri... Listen, I've been all over this with your ambassador. It is not a trick... Well, I'll tell you. We'd like to give your air staff a complete run-down on the targets, the flight plans, and the defensive systems of the planes... Yes! I mean i-i-i-if we're unable to recall the planes, then... I'd say that, ah... well, ah... we're just gonna have to help you destroy them, Dmitri... I know they're our boys... All right, well listen now. Who should we call?... *Who* should we call, Dmitri? The... wha-whe, the People... you, sorry, you faded away there... The People's Central Air Defense Headquarters... Where is that, Dmitri?... In Omsk... Right... Yes... Oh, you'll call them first, will you?... Uh-huh... Listen, do you happen to have the phone number on you, Dmitri?... Whe-ah, what? I see, just ask for Omsk information... Ah-ah-eh-uhm-hm... I'm sorry, too, Dmitri... I'm very sorry... *All right*, you're sorrier than I am, but I am as sorry as well... I am as sorry as you are, Dmitri! Don't say that you're more sorry than I am, because I'm capable of being just as sorry as you are... So we're both sorry, all right?... All right.

Good ones, Kyle and CWGW. That scene in Lost Highway is classic Lynch. And Strangelove is one of my top 5 movies of all time. Both will get the Daily Dialogue treatment!

all mike leigh films have real good phone conversations. I'm sorry that I can't think of one specific one right now.

Technically, Colin Farrell *is* on the phone for this memorable speech he delivers to the crowd in Phone Booth:

Stu: I have never done anything for anybody who couldn't do something for me. I string along an eager kid with promises I'll pay him money. I only keep him around because he looks up to me. Adam, if you're watching, don't be a publicist. You're too good for it. I lie in person and on the phone. I lie to my friends. I lie to newspapers and magazines who, who sell my lies to more and more people. I am just a part of a big cycle of lies, I should be fuckin' president. I wear all this Italian shit because underneath I still feel like the Bronx. I think I need these clothes and this watch. My Two thousand dollar watch is a fake and so am I. I've neglected the things I should have valued most. I valued this shit. I take off my wedding ring to call Pam. Kelly, that's Pam. Don't blame her. I never told her I was married. And if I did she, she would have told me to go home. Kelly, looking at you now, I'm ashamed of myself. Allright? I mean, work so hard on this image, on Stu Shepherd, the asshole who refers to himself in the third person that I only proved I should be alone. I have just been dressing up as something I'm not for so long, I'm so afraid no one will like what's underneath. But here I am, just flesh and blood and weakness, and uh and I love you so fucking much. And, um, I take off this ring because it only reminds me of how I've failed you, and I don't, don't want to give you up. I want to make things better, but it may not be my choice anymore. You deserve better.

The Big Sleep:

[making a prank phone call]
Philip Marlowe: What can I do for you? I can do what? Where? Oh, no, I wouldn't like that. Neither would my daughter.
[hangs up]
Philip Marlowe: I hope the sergeant never traces that call.

There are several hilarious phone conversations in "It's a Mad, Mad, Mad, Mad World". One of the best is this one with Dick Shawn (Sylvester) and Ethel Merman (Mrs. Marcus):

Sylvester Marcus: [into a phone] Mama, who's with you? Where are you talking to me... Where are you?
Mrs. Marcus: [into the phone] I'm with this truck driver at Peterson's garage in a place called Plaster City. And will you just shut up a minute so I can tell you what happened!
Sylvester Marcus: Now listen, Mommy, you listen to me close. You stay right there, because I'm coming, Mom. I'm coming to get you right now.
Mrs. Marcus: Will you SHUT UP AND LISTEN?
Sylvester Marcus: Mama, it's alright. Everything's gonna be alright. Your baby's coming to get ya. You just sit there. Sit there, relax, take it easy. I'm coming to get you, Mama! Everything is gonna be alright!
[Hangs up]
Lennie Pike: Well?
Mrs. Marcus: So he's coming here. And I'm not to worry about a thing, because "everything is going to be alright!"
Mrs. Marcus: [to Emmeline] Exactly like your father: a big, stupid, muscle-headed moron!

http://www.youtube.com/watch?v=wX12Xk9WFjw

Pulp Fiction:

Lance: [answering the phone] Hello.
Vincent: Lance! It's Vincent. I'm in big fuckin' trouble, man. I'm coming to your house.
Lance: Whoa. Whoa. Hold your horses, man. What's the problem?
Vincent: I've got this chick, she fuckin' O.D.in' on me!
Lance: Well, don't bring her here! I'm not even fuckin' joking with you, man! Do not be bringing some fucked-up pooh-bah to my house!
Vincent: No choice.
Lance: She's O.D.in'?
Vincent: She's fuckin' dyin' on me, man!
Lance: Okay, then you bite the fuckin' bullet, take her to a hospital and call a lawyer.
Vincent: Negative.
Lance: This is not my fuckin' problem, man! You fucked her up, you fuckin' deal with this!

Probably a whole separate category: messages on answering machines.

"The Hangover"

Phil Wenneck: [his answering machine message] Hey, this is Phil. Leave me a message, or don't, but do me a favor: don't text me, it's gay.

This isn't even a phone conversation and it's corny but also thought-provoking and seeing as Valentine's Day is coming up...

"Love, Actually"

Prime Minister: [People say] we live in a world of hatred and greed, but I don't see that. It seems to me that love is everywhere. Often, it's not particularly dignified or newsworthy, but it's always there - fathers and sons, mothers and daughters, husbands and wives, boyfriends, girlfriends, old friends. When the planes hit the Twin Towers, as far as I know, none of the phone calls from the people on board were messages of hate or revenge - they were all messages of love. If you look for it, I've got a sneaking suspicion... love actually is all around.

Not too many phones on a space station, but the intercom conversation Han has on the Death Star makes me smile every time I see it:

[Han answers the intercom after comandeering an attack station]
Han Solo: [sounding official] Uh, everything's under control. Situation normal.
Voice: What happened?
Han Solo: [getting nervous] Uh, we had a slight weapons malfunction, but uh... everything's perfectly all right now. We're fine. We're all fine here now, thank you. How are you?
Voice: We're sending a squad up.
Han Solo: Uh, uh... negative, negative. We had a reactor leak here now. Give us a few minutes to lock it down. Large leak, very dangerous.
Voice: Who is this? What's your operating number?
Han Solo: Uh...
[Han shoots the intercom]
Han Solo: [muttering] Boring conversation, anyway.

http://www.youtube.com/watch?v=XluKcRSlXAw