
This episode is so funny in so many ways. Darin Morgan excels in writing the hilarious. I think the only way I can get through this one is in point form or something, so bear with me.
Let's do some funny quotes first (you can go ahead and call me lazy- I'm two whole discs behind in my reviews, so do you want them or not? ;P I mean, as if I'm going to be as entertaining as the actual episode here):
PHOTOGRAPHER: They say the eyes capture the last image the murder victim sees before they're killed.
CLINE: So what do they say about the entrails?
PHOTOGRAPHER: Yuck.
(presumably talking about Mulder)
CLINE: This guy's supposed to be an expert at this sort of thing.
HAVEZ: I heard he was a bit... unorthodox.
CLINE: He comes highly recommended.
HAVEZ: Yeah. I saw him on TV.
CLINE: Hey, so he's a publicity hound. As long as he gets results.
PHOTOGRAPHER: I once worked on a case he did. Very spooky.
CLINE: As long as he gives us leads, I don't care how big a kook.
(Mulder walks in, they stare at him)
CLINE: Who the hell are you?
CLINE: You believe in this stuff?
M: I'm not convinced of its accuracy but I'm pretty sure the victim was.
CLINE: Why?
M: Her leaves were telling her she was about to be murdered.

YAPPI: You give off negative energy.
M: I can assure you, Mister Yappi, I'm a believer in psychic ability.
YAPPI: So you say with your mouth but your thoughts tell me the truth.
CLINE: Agent Mulder, please.
S: I can't take you anywhere.

CLINE: Look, all I know is that so far, Yappi has provided more solid, concrete leads on this case than you have. Now, if you don't mind, I have to get an A.P.B. out on a white male, age seventeen to thirty-four, with or without a beard, maybe a tattoo... who's impotent. Let's go.
S: Might as well go home, Mulder, this case is as good as solved.

CLINE: It's kind of creepy, isn't it? The Stupendous Yappi said the first victim's body would be dumped somewhere, then we find it in a dumpster.
M: Oooh, I just got a chill down my spine.
Clyde essentially recreates the entire Stupendous Yappi scene, leaving Scully skeptical to say the least. He finishes on the so called 'rape' Yappi mentioned:
CLYDE BRUCKMAN: Oh, no, no, no, not at all. In fact, she's instigating the whole thing.
M: Then what's wrong?
CLYDE BRUCKMAN: Oh... sometimes, it... it just seems that everyone's having sex except for me.

M: Mister Bruckman, can you tell us why the killer is murdering people in the way that he is?
CLYDE BRUCKMAN: Why does anyone do the things they do? Why do I sell insurance? I wish I knew. Why did this woman collect dolls? What was it about her life? Was it one specific moment where she suddenly said, "I know... dolls."

PS; that doll that Mulder is gripping so tightly is almost certainly the same creepy one from season five's Chinga.
CLYDE BRUCKMAN: Do you want to know how you're going to die?
M: Y, yes, I would.
CLYDE BRUCKMAN: No, you don't. Of course, not knowing has its own drawbacks which is why a good insurance policy is so important. I, I don't know what kind of coverage the F.B.I. has, but, uh, General Mutual has...
M: Then if the future is written, then why bother to do anything?
CLYDE BRUCKMAN: Now you're catching on.
M: Mister Bruckman, I believe in your ability but not your attitude.
...
CLYDE BRUCKMAN: Well, you see, that's another reason I can't help you catch this guy. I might adversely affect the fate of the future. I mean, his next victim might be the mother of the daughter whose son invents the time machine. Then the son goes back in time and changes world history and then Columbus never discovers America, man never lands on the moon, the U.S. never invades Grenada...Or something less significant... resulting in the fact that my father never meets my mother and consequently, I'm never born.
(Pauses. Changes his mind; that is appealing to him!)
So when do we start?
M: Do you receive any other impressions from it (awful toad door stopper)?
CLYDE BRUCKMAN: It's ugly. Next.
...
CLYDE BRUCKMAN: I got it! This is yours. This is from your New York Knicks t-shirt! (Beyond the Sea reference!)

M: How are you receiving this information about the body's location?
CLYDE BRUCKMAN: How should I know?
M: I mean, are you seeing it in a vision or is it a... sensation? How do you know where to go?
CLYDE BRUCKMAN: I just know.
M: But how do you know?
CLYDE BRUCKMAN: I don't know!

(Mulder gives him a piece of lace in a small evidence bag.)
CLYDE BRUCKMAN: What's this?
M: The only evidence recovered from Claude Dukenfield's body. That fiber may have come from something the killer was wearing at the time of the crime.
CLYDE BRUCKMAN: Don't you have crime labs that analyze these things for you?
S: (directly at Mulder) Yes! Yes, we do.

M: Get this, Scully. The lab analysis from the first bit of fiber that was found just came back. It's lace.
S: Chantilly lace?
MULDER: You know what I like.

(both ridiculously amiable)
PUPPET: They brought you right to me, right to where I work.
CLYDE BRUCKMAN: What are the chances of that happening?
PUPPET: They're astronomical! It's beyond believability.
CLYDE BRUCKMAN: But not impossibility. I mean, after all, here we are.
PUPPET: It's funny how things work out sometimes, isn't it?
CLYDE BRUCKMAN: I'll say.
PUPPET: So there's something I've been wanting to ask you for some time now...

...
CLYDE BRUCKMAN: No. You don't kill me now.
PUPPET: I don't? Why not?
CLYDE BRUCKMAN: How should I know?
Actually he does know. He's been seeing visions of his own death; in fact, seems to be probably looking forward to it. He's planning on killing himself. It's a somewhat tragic fate; he leaves a note on the door:

S: "My neighbor, Mrs. Lowe, passed away last night. Please see that the remains of her remains are taken care of. Would you like a dog? He's paper-trained and well-behaved, regardless of his actions last night, which you can't really blame him for."
Ie the dog was starving, and ate his owner after she died. Neat for a Pomeranian.

S: (finally giving in to temptation) All right. So how do I die?
CLYDE BRUCKMAN: You don't.
Wow, this sparked, and continued to spark some crazy discussion in the XF world. We can't help but take that to be true, and I think often with later episodes, the writers found ways to subtly refer back to this (I am thinking specifically of season six's Tithonus, the classic example where Scully is slated to die, is shot, then lives miraculously).
Scully. Never. Dies.

In fact- how many different times has Mulder 'died'. It already happened once this/last season. I can think of at least three other times right off the top of my head where Mulder dies or "dies", and frankly, there are probably more. Aside from a near-death experience in One Breath (not an assumed-death, nor an actually-death-then-brought-back-to-life gimmick) I can't think of a single case where Scully dies or "dies".
This could even be seen as the episode that planted the Scully-as-Holy-Mother seed. In that way, that one simple two-word line is a total game-changer for the show.