The fact that you NEED a knife isn’t the same as having a good reason to EXPECT one. That’s the key difference as far as I’m concerned. The definition Larry cites has become the one used most by the populace at large, but it’s a much less precise meaning (and you can find many people, not just robots like Bender, who say that it’s not really irony). By that definition any almost surprising outcome is ironic.
The need for / expectation of something has nothing to do with it.
Is my second example (cans, no opener) ironic? How about my Simpsons one, in my first post in this thread? Is that ironic? How about the famous Twilight Zone ending where the last man on earth, who loves to read, ends up in a library but with broken glasses?
I think all of these are ironic, and they all fit the general definition of the actual events mocking one’s sense of what ought to be. There ought to be a knife, an opener, the marshmallow truck ought to be soft, the man ought to be able to read.
I think I’ve just used the word “ought” more in the last two lines than I have in my entire life.
I guess it comes down to this: definitions change according to popular usage, and these days irony has come to fit some situations that it wouldn’t have previously included. Bender is using the older definition, by which the other stuff - the stuff the Robot Devil likes so much and also references in his first appearance on the show - isn’t ‘real’ irony.
It’s worth pointing out that the only reason it’s in the dictionary, is that people like Alanis so consistently misuse it.
The last example that Bender gives is irony in its simplest form: The sentence deliberatly constructed to convey a meaning that was not the meaning intended. The fact that it was essentially impossible for anyone but the Robot Devil to pick up on the irony (being “sneaky”) is irrelevent. Sarcasm is a cheap form of irony. Jonathan Swift’s satire, “A Modest Proposal” employs irony. No permutation of trachaeotomy patients and spoon factories is, traditionally speaking, ironic. None of the verses in Alanis Morrisette’s song are ironic, although you could argue that the chorus is.
That said, the fact of the matter is that usage determines meaning, not the opposite. All the stuff Robot Devil said was ironic really were ironic, because irony no longer only means “The use of words expressing something other than their literal intention.” It now also means “A condition of affairs or events of a character opposite to what was, or what might naturally be, expected; a contradictory outcome of events as if in mockery of the promise and fitness of things.” Because that’s how most people use it. And I think this is a good thing, because we need a term to describe the second definition more than we need a term to describe the first.
So if the spoons were made of iron, that would be ironic. 
Perhaps the Robot Devil was made of iron while all the other robots were made of some other metal, so when it turns out that Fry is to get the Robot Devil’s hands it is, in fact, ironic.
If that were the meaning RB intended when he said it was ironic, then the statement would indeed be ironic. If he meant it the literary sense, then it wasn’t. See? Simple.
There are (at least) two definitions of irony. One is more like what most people call sarcasm. That is the definition Bender is referring to.
However, generally with this form of irony, you aren’t being deliberately deceptive. For instance, if you were to say “You’re a real genius, aren’t you?” with a sarcastic tone to someone who’s being an idiot, that would be ironic. But you aren’t trying to trick them – you want them to understand that they’re an idiot. I don’t think the robot devil’s deception of Leela qualifies. Not just because he’s deliberately deceptive, but because what he says is literally true, it’s just not what she thought he meant.
The other definition of irony is when a situation goes against your expectations. I’m explaining it poorly, but hopefully you know what I mean. The wheel landing on the robot devil after he had told Fry “I’m sure it won’t land on anyone you know” in a way that indicated he believed it would land on Bender was ironic, in my opinion. If it had just landed on the Robot Devil without him intending and expecting it to land on Bender, then it wouldn’t have been ironic, just coincidental as Bender said.
The scheme where he deafens Leela isn’t ironic, because it was all planned to happen that way. So at least for the Robot Devil it was perfectly in line with his expectations.
Well you have to remember that Bender is 30% iron.
Marley23:
It’s not nonsense. It may not be ironic, but it’s still in line with the other examples in the song to want to go somewhere, pay for a ticket, and then, before the trip, discover that you could get there for free. (And presumably the ticket is non-refundable)
If she’d explained it as you did, I agree, it wouldn’t be nonsense. Even if she’d sang “It’s finding out the ride could’ve been free when you’ve already paid,” it would have fit the bill. But that isn’t what she says. She just says “it’s a free ride when you’ve already paid.” We don’t know that the ride was originally offered for free or something, and we don’t know that it’s an actual mode of transportation or a figurative “free ride.” The way she says it doesn’t make sense - it’s NOT a free ride if you’ve already paid.
I would say the spoon example could be ironic because you would normally expect to find knives and spoons together – so you’d think something like “Oh good! A spoon, there will obviously be a knife near here. Damn, not in this case.”
I don’t think the free ticket example is ironic, unless they’re more linked that mentioned, but I think it makes perfect sense. Yes, the ride isn’t free, but you can still say you were being offered a free ride.
The “hand in marriage one” – I’m not convinced. If “irony” really used to mean “words contrary to actual meaning,” then OK, but I don’t think anyone has said this, they’ve just said that the dictionary says something like that – which I think is a simplification of “contrary words carrying that meaning.” Like, if I say “Yeah, I’m sure you’re really smart” sarcastically (irony? sarcasm, anyway) vs. not sarcasticly, which is just lying.
But you weren’t offered a free ride. You found out about it later (that expectation thing again). Which would make you go “aww, dammit!” - and that’s the standard for irony she uses. 
That IS what irony means (it’s not ‘used to’). That’s why that definition is in the dictionary in the first place, and a bunch of us have said that. The Robot Devil is not lying. He does want her hand - he just doesn’t want to chop it off. He wants it in the metaphorical sense of ‘taking someone’s hand in marriage.’ If you tell someone “you’re smart” when you don’t, that’s lying. If you say “you’re smart” while indicating with your tone of voice that you don’t think that’s really true, then you’re being ironic. Beezlebot does something more complicated, but he’s still using the words to mean something non-literal.
Granted this is The Straight Dope Message Board, where we make more stretches than Richard Simmons - but let’s face it, these are giant reaches. If you’re a surgeon doing a tracheotomy in a spoon factory instead of, say, a hospital, you’re a moron. 
In any case shall we say it’s highly doubtful Alanis (or Glen Ballard, who probably wrote the damn song) were thinking of such an involved scenario when this piece of crap was put to paper. Neither of the above are ironic to begin with, but even if it’s possible to somehow twist the original line into an irony, it won’t be in a context resembling the original (although I admit we don’t know EXACTLY what was meant when the song was written - yet another one of its faults). In other words, you guys are using the words to convey something other than their real intention - so your interpretations are ironic.
To quote my closer personal friend*, comedian Ed Byrne:
*Well OK, vague personal acquaintance.
The contrary-words definition from the OED is "A figure of speech in which the intended meaning is the opposite of that expressed by the words used; usually taking the form of sarcasm or ridicule in which laudatory expressions are used to imply condemnation or contempt. "
I interpreted that to mean that the meaning conveyed, as of speaking, is different; not that a later revealed meaning is different. I expect I was making a mistake… however, to help me understand you, can you think of any more examples where the meaning contradicted by the words isn’t evident in their saying, but is ironic rather than just confusing or lying?
Not offhand- you don’t see it in real-life much (it’s in TV and the movies all the time). The Devil isn’t lying - he really does want Leela’s hand. Well, not really, it’s a bargaining chip to him. But he’s doing the very typically Devil-ish thing of “ah-ha, you’ll see how foolish it is to take me at my word when I’m going to twist it later.”
Ready for a simple conclusion to this discussion? Good, neither was I. It occurs to me that this may be ironic to us without being ironic to Bender.
As the audience, having seen many similar Faustian bargains go awry on TV, we expect Bender’s name to come up. (I watched this episode a few days ago, and my roommate said “It’s gonna be Bender” as he wandered by the TV.) The show cleverly plays with that, since Bender’s name is the last one before the Robot Devil’s and the spinner pauses on it for a moment. Then we get the surprise of the spinner moving one more notch. So it’s not what we expected, because we expected the ‘surprise’ selection of Bender. The Devil, having done this sort of thing before, probably thinks it should be Bender as well, since he’s very into the whole irony thing.
Bender, though he’s probably watched a lot of The Scary Door, has different expectations - he doesn’t anticipate the cliche outcome because he’s not that self-aware. So to him, it’s just a coincidence that the Robot Devil loses instead.
jjimm, Ed Byrne sounds hilarious. Any way an American such as myself can get my hands on some of his stuff?
I say it’s lying. Though I haven’t seen the episode, so correct me if I’m misinterpreting. Robodevil says “blah bah blah Leela’s hand blah” which he knows and intendeds that everyone will think mean literal hand. The fact that in a different context, it turns out to mean something else doesn’t make it not lying. The fact that the statement is interpretable in different ways might make it irony – we’re still discusssing that.
But ‘lie’ isn’t just what the sentance means out of context, communication includes context.
Assuming I don’t have him confused with another Irish stand-up, I believe he’s been a on the Conan O’Brian show a few times.
The last line of the second verse of Ironic:
And as the plane crashed down, he thought, “well, isn’t this nice?”
That was a rather ironic thought, dont ya think?