Examples:

1. There must be life elsewhere in the universe, otherwise the universe would be a lonely and unappealing place.
2. Science must be able to explain everything we see. If it can't we could never really be sure of anything.

The New England Skeptical Society wrote up a great document about the Top 20 Logical Fallacies at http://www.theskepticsguide.org/resources/logicalfallacies.aspx. For Agrument from Final Consequences, they wrote:

Such arguments (also called teleological) are based on a reversal of cause and effect, because they argue that something is caused by the ultimate effect that it has, or purpose that is serves. For example: God must exist, because otherwise life would have no meaning.

the world would be a better place if people everyone knew what this means so we should teach them

would be an example

I'll throw in an answer just to stir the pot, although there are good ones listed already. This fallacy (as used by skeptics) is more commonly referred to as the Appeal to Consequences. (I found some indications that "appeal to final consequences" might simply indicate a conclusion drawn from an argument where the conclusion is not a consequence of the previous logical steps, which are themselves valid.)

From The Nizkor Project:

The Appeal to the Consequences of a Belief is a fallacy that comes in the following patterns:

1. X is true because if people did not accept X as being true then there would be negative consequences.

2. X is false because if people did not accept X as being false, then there would be negative consequences.

3. X is true because accepting that X is true has positive consequences.

4. X is false because accepting that X is false has positive consequences.

5. I wish that X were true, therefore X is true. This is known as Wishful Thinking.

6. I wish that X were false, therefore X is false. This is known as Wishful Thinking.

This line of "reasoning" is fallacious because the consequences of a belief have no bearing on whether the belief is true or false.

So, this form of argument supports a presupposed conclusion because the proponent would simply not like it if their conclusion were wrong; but of course preferring a conclusion does not render that conclusion true. The net outcome is the argument carries no weight.

One might look more broadly to say that many claims that skeptics reject have this fallacy at their heart, and other fallacies are employed in order to lend legitimacy to the otherwise falsified claims, especially use of anecdotal evidence, subjective evaluation, and cherry picking.

There are a lot of good examples given in the other answers. Here's another example: "Of course there is karma. A universe without karma would be unfair."

This presupposes that the universe operates according to a system of karma, because the arguer does not like to entertain the consequences of this not being the case.

Here are a few others as quoted from my source, apologies for any duplication:

• "God must exist! If God did not exist, then all basis for morality would be lost and the world would be a horrible place!"

• "It can never happen to me. If I believed it could, I could never sleep soundly at night."

• "I don't think that there will be a nuclear war. If I believed that, I wouldn't be able to get up in the morning. I mean, how depressing."

• "I acknowledge that I have no argument for the existence of God. However, I have a great desire for God to exist and for there to be an afterlife. Therefore I accept that God exists."

And some more from Wikipedia:

• "Pi is probably a rational number: being rational would make it more elegant."
• "Real estate markets will continue to rise this year: home owners enjoy the capital gains."
• "Humans will travel faster than light: faster-than-light travel would be beneficial for space travel."
• "Santa exists, or you won't get any presents this year!"
• "The axiom of choice must be wrong because it implies the Banach-Tarski paradox, meaning that geometry contradicts common sense."
• "Free will must exist: if it didn't, we would all be machines." (also a False Dichotomy)
• "If the six men win, it will mean that the police are guilty of perjury, that they are guilty of violence and threats, that the confessions were invented and improperly admitted in evidence and the convictions were erroneous... This is such an appalling vista that every sensible person in the land would say that it cannot be right that these actions should go any further." Lord Denning in his judgment on the Birmingham Six.

One I've heard just recently is that pregnancy shouldn't be considered a risky medical condition because it will lead to doctors being condescending and taking choices away from pregnant women. Even if that were the case, that wouldn't make pregnancy any less risky than it actually is. It just doesn't make sense to me to risk your health and that of your baby just to spite some doctors.

rjstelling,

"God must exist, because otherwise life would have no meaning."

Don't dismiss "Science must be able to explain everything we see. If it can't we could never really be sure of anything."