In most of her appearances, Bethany Horowitz overhears Denny Crane saying something inappropriate because he hasn't noticed her arrival. He only notices her after the person he's conversing with (usually Alan Shore) suggests that he look down.

Here is a list of the occurrences of this running gag:

• In 3x02 [New Kids On The Block], Alan and Denny are in the break room talking about his date with Bethany:

Alan Shore: What was she like otherwise?
Denny Crane: A—a—an attractive head, nice breasts, and that was pretty much it—breasts and a head.
Alan Shore: How did you leave it?
Denny Crane: I just left. I didn’t know what else to do; I just walked out.
Alan Shore: Do you think it’s possible she could have followed you here?
Denny Crane: Well, I don’t think so. Why?
Alan Shore: Well . . .
Alan Shore looks down. Bethany Horowitz is standing between them, and smiles up at Denny Crane, who also looks down.
Bethany Horowitz: I didn’t want to leave things on a bad note, so I wrote you a little note.
Denny Crane: Oh?
Bethany Horowitz: Actually, it’s a summons and complaint.

• In the balcony scene of 3x03 [Desperately Seeking Shirley], Denny is again talking about Bethany:

Denny Crane: Her nickname is "The Badger". I wonder if she’s a badger in the sack. Oh. Could be painful.
Alan Shore: Do you think she’d mind you talking about her this way?
Denny Crane: No idea. Why?
Alan Shore: Well, perhaps you should look down, Denny.
Denny Crane: Do not tell me.
Alan Shore: Oh, yes.
Denny Crane: No.
Alan Shore: Yes.
They both look down at Bethany.
Bethany Horowitz: Having a greater appreciation for who, and what you are, I’m not offended.
Denny Crane: You snuck up on me.
Bethany Horowitz: No. I came to tell you that the court assigned a trial date.

• In 3x05 [Whose God Is It Anyway?], Denny is talking to Shirley about his encounter with Gracie Jane:

Shirley Schmidt: You had sex with her.
Denny Crane: Cheap sex—the best kind.
Shirley Schmidt: What about Bethany? Wouldn’t she object?
Denny Crane: A gentleman never tells.
Shirley Schmidt: A gentleman might want to look down.
Denny Crane: No way.
Shirley Schmidt: Way.
Denny Crane: smiling down at Bethany Horowitz I knew you were there. I was just trying to make you jealous.
Bethany Horowitz looks very hurt, and exits angrily.
Shirley Schmidt: Denny, if she’s going to be the seventh one, you might want to go after her.
Denny Crane: facing the inevitable, turning to follow her. Pumpkin—

• In the balcony scene of 3x06 [The Verdict], Denny has a talking "Gracie Jane" doll in his pants.

Alan Shore: How are things going with Bethany?
Denny Crane: Three dates. Big one coming up.
Alan Shore: You think she’d be upset if she discovered Gracie Jane in your pants?
Denny Crane: No idea. Wh—?
Alan Shore looks sheepish.
Denny Crane: Not a chance.
Alan Shore: Oh, yes.
Denny Crane: Don’t lie to me.
Alan Shore: Scout’s honor.
Denny Crane: I am not looking down.
Alan Shore: But you must.
Denny Crane looks down to see an angry Bethany Horowitz, who pulls the string.
Gracie Jane Doll: Guilty, guilty, guilty.
Bethany Horowitz: I don’t date disgusting, vile pigs!
Alan Shore: In the doghouse again.
Denny Crane: I gotta get that woman a pair of squeaky shoes.
Alan Shore: You wanna go after her?
Denny Crane: In time. She’s gotta learn not to interrupt my special time.

• In 3x07 [Trick Or Treat], Denny and Alan are discussing Bella's revelation that Denny may be Bethany's father.

Alan Shore: Is she sure?
Denny Crane: No. I'm gonna have to have a paternity test. Can two full-sized people have a midget?
Alan Shore: Does Bethany know?
Denny Crane: I dunno. God. It's one thing to date a dwarf, but ... to have fathered one?! Oh!
Alan Shore: Denny, I bet Bethany knows now.
Denny Crane: Oh .... God!
Alan Shore: Afraid so.
Denny Crane: Hi, Honey. Who's your daddy?

Many thanks to Imamess and Sheri for their transcribing efforts, from which these snippets of dialogue were pulled.