Occasionally, musicians from a number of different bands may come together and form a "supergroup" with the overall hype being that the sum of the supergroup's parts are better than the original bands they came from (i.e. Velvet Revolver, Audioslave), only for it all to end up being unlistenable rubbish.
Cirque du Soleil and Criss Angel are both popular, so it was believed that a collaboration between the company and the magician on a Las Vegas magic show was money in the bank; instead, Criss Angel BeLIEve required a massive Retool to keep running.
The Simpsons - Sideshow Bob's plan to kill Bart at Five Corners
The classic trick question "which is heavier, a ton of feathers or a ton of lead?" works because of this fallacy; the hope is that the person answering will think that because individual feathers are light, a measured weight of them would be lighter than the same weight of something normally thought of as "heavy."
Some trick questions go even further and make the feathers the right answer, by using different measures of weight.
One memorable variant uses the word "pound", then goes on to discuss the economic trends of the United Kingdom.
A pound of gold weighs less than a pound of feathers because gold is measured in troy weight.
Internet filters rely on this trope. Imagine why Pakistan blocked all of Facebook because of just one group.
The same is true of word filters: written erotica may mention breasts, but blocking all uses of the word blocks out gynaecology, chicken recipes, and other innocent uses. The "Scunthorpe Problem" nets even more collateral blocking (while the devious perverts just use word-substitution tricks).
Alternative health claims are rife with these. The claimants will say that X is in a drug/food/compound, and therefore that the substance is healthful/unhealthful. For example, one fad claims that Splenda is toxic because it contains the element chlorine. It does. So does table salt. That's a classic example of this fallacy. A less unreasonable claim is that chloro-carbons (like Splenda) are unhealthful, while ionic chlorine (such as salt) is fine. This claim does not run afoul of this fallacy, though "Splenda is toxic at any reasonable dose" is not accepted by mainstream evidence-based medical practitioners. Food additives go through extensive toxicity testing before approval.
A list of sports examples could probably be its own wiki - and you'd probably have to have a different wiki for every sport! Suffice it to say, "we're the best team in the league, therefore by signing the best player we'll get better" has been a prevalent attitude throughout the history of sport. Sometimes, yes, it pays off. A lot of times...it doesn't.
The Paradox of Thrift is an economic concept based on this. The fallacy assumes that typically, it is better for an individual to save, increasing his/her financial capital, allowing that individual to invest and improve his/her lot. But if everyone saves, then because no one is consuming, businesses have to contract and lay off workers, slowing the economy and making everyone worse off. What's good for the individual (saving) isn't good for the economy in the aggregate.