Smoking Gun Control

Easy ways to solve crimes will quickly be eliminated. CCTV cameras were broken, guns and cars were stolen, etc. Anytime it does look like a vital piece of evidence has been found early on it will either be quickly contradicted or somehow made inadmissible in court.

This is because easy-to-solve crimes wouldn't be to entertaining to watch. (One can assume that they happen between episodes, when we're not watching.) Also, smart criminals (who take precautions to cover their tracks) are more interesting characters than dumb ones.

Anime and Manga

 * Double Subversion: Majin Tantei Nougami Neuro (it's like Scooby Doo with a devil instead of a dog, and lots more murder) features a killer who is clearly caught on CCTV committing the crime, carrying the murder weapon which is found on her person, and who had prominent, obvious connects to her victims . Yet somehow, the police are still unable to solve the crime (something to do with the crystal clear CCTV evidence, motive, lack of alibi, and clear connections to the victims being inadmissible in court!)

Comic Books

 * Bookhunter: The thief Kettle Stitch is very good about this. Agent Bay realizes that an otherwise-perfect book theft has resulted in a missing circulation card that can be linked to Kettle Stitch's library card. Except Kettle Stitch anticipated this, and used a counterfeit copy of someone else's card, instead of her own. So Agent Bay investigates how said library card was counterfeited, and finds that Kettle Stitch hacked into the library's patron records computer system—but his attempt to trace her location fails, and she just erases all the evidence of her hacking from the system.

Literature

 * In the novel and movie Rising Sun the security cameras should make solving the case easy. Except the one video tape of the crucial time and place is missing, and when it's returned, it turns out to have been tampered with.
 * In the Lord Darcy stories, a character once comments that detective work in cities would be a lot easier without all the anti-scrying spells placed on homes and businesses. Darcy comments that if these were not there, detective work would be non-existent - you could just call in a journeyman sorcerer to use some basic divination spells and the case would be solved in under an hour. He also mentions that this would also eliminate all hope of personal privacy, as any interested mage could scry into your house or office whenever they wanted (This is the reason that anti-scrying spells are placed on homes and businesses in the first place).
 * In Dorothy L. Sayers's Busman's Honeymoon, the clues to the murder are all there when Wimsey and Harriet arrive at their new house, but it's dark, and they have to have the chimneysweep in the next day and "all the clues got destroyed in the muddle". Or if they weren't, they're removed in the cleaning-up process - some by the murderer, under the eyes of the sleuths!

Live Action TV

 * Happens in a noncriminal example in House in which if anyone is cured quickly near the beginning they'll only get worse or not be the patient of the week. Justified, since these are specialists and the perfectly nice local GP can handle the simple (boring) cases.
 * Pushing Daisies: the dead person (almost) never has complete or accurate information about the killer. The one time the victim says "My wife did it", he's a polygamist.
 * In the second season, Gustav Hoffer knew who killed him, but was so busy talking about something else that his minute ran out. Rollie Stingwell also gave them an actual name, but . Erin Embry knew who her killer was, but.
 * Used frequently in Law and Order where the important evidence usually does exist, but legal mistakes in handling it means it can't be admitted in court.
 * Often beaten into the ground by the various L&O franchises, where multiple pieces of evidence are tossed for various (occasionally contradictory) reasons. The worst offender was arguably the Law and Order SVU season 8 finale, "Screwed" where more or less ALL the evidence against the defendant was tossed because of a corrupt cop at the evidence room tipping the defense off to "questionable practices" in gaining the evidence, then "losing" the rest.
 * This was often averted in the very early days of Law and Order "Prime." There would be some ambiguity back then about whether some defendants were actually guilty. Eventually either the producers or the audience decided they wanted certainty, so after, say, season three the cops always find damning evidence that gets thrown out of court.
 * Very rare on Criminal Minds. Evidence found is usually pertinent and useful (they just don't always know what it means).
 * Rare on CSI, which can fingerprint the air.
 * There was one episode in which a literal truck load of evidence was stolen in the first five minutes. They got it back, but the chain of custody was broken so none of it could be admitted.
 * A skit on The Mitchell and Webb Look involved the police trying to find the "Identity Killer". He, among other things, put t-shirts with a photograph of himself on his victims, left his driver's license and passport on the scene, and hung out at the police station while detectives debated the case.

Video Games

 * This seems to happen to Phoenix Wright: Ace Attorney in Every. Freaking. Case.
 * Particularly notable towards the end of the first game where everyone in the court watches a security camera video and then Phoenix and the prosecutor freak out when it turns out that the most important parts of what happened are not shown. This is also a justified instance, as
 * Also, if the crime has any direct witnesses, they will almost always turn out to have completely misinterpreted what they saw.
 * And any seemingly-critical photograph taken of the crime will turn out to be entirely misleading.