War Is Hell. Anti-war works suffer badly from this. François Truffaut once said that "There is no such thing as an anti-war movie" because it will invariably look exciting up on screen. Another old saying is; "Soldiers love anti-war movies but never the way the maker wants", though these descriptions actually apply to war in other media as well as film. Plus, Truffaut's theorem isn't the only problem. Even if the work is intended to show how horrible war is it almost always backfires. While certain aspects of the war can be portrayed negatively, it's near impossible to make a work that is completely anti-war, regardless of what approach the creator takes, to the point where trying to make an anti-war work is nothing short of futile. There's a couple of reasons for this;
Even if #1 is avoided, and the work doesn't show any fighting and instead focuses on other negative aspects of war, such as the suffering of civilians or atrocities committed by one of the sides, it's a bit difficult to get the message across. Without showing the fighting, which is the actual war part of anti-war, the work can't actually show why the civilians are suffering or why the belligerents are committing these horrible crimes.
While the war itself is meant to be seen negatively, the works often go out of their way to portray at least one side fighting it in a positive light. In addition to seeing the troops fighting cool battles, the audience sees them committing selfless acts of bravery and maintaining strong willed attitudes of hope and perseverance. So the very fact that war sucks brings out the best in people.
Even if #3 is avoided and the work does focus excessively on the negativity of war besides just the battles, and shows demoralized troops driven committing horrible atrocities, there will inevitably be at least one character who withstands it and never breaks. So no matter how bad the war gets, hope always survives.
A.) If only one side involved is like this, then it's only anti-war for that side. It's extremely pro-war for the other side because all it's done has justified them fighting, and the audience wants them to fight against the evil side.
The only time this doesn't happen are war survivor/refugee films, especially if the cast are survivors of a genocide and the enemy is an unstoppable tide of death and destruction and there is little to no talk of "fighting back" and instead is constantly on the run.
Another type of war film that generally averts this are nuclear holocaust movies like WarGames and The Day After (played seriously, that is; Dr. Strangelove is one of the most notorious cases to play this trope straight because it's a comedy). They often don't show battles and the whole futility of nuclear warfare elevates the conflict to an Enemy Mine between the mutually antagonistic powers to prevent The End of the World as We Know It. If the missiles do start flying, expect to see death, destruction, misery and the horrifying end of humanity as people slowly die of radiation poisoning.
Junk food is one of those things that it is hard to have An Aesop about because of how colorful and tasty it always looks. Any diet commercial will backfire horribly if they show the foods you shouldn't be eating and say that you shouldn't be eating them.
British TV chef Jamie Oliver tried to avert this by showing people their weekly intake of junk food all dumped together into a huge unappetizing mess. As Charlie Brooker pointed out, the resulting message was "don't eat your food that way".
This backfired again on Jamie Oliver as he tried to explain to children why chicken nuggets made from mechanically separated poultry are terrible and non-nutritious, as he carefully cut up a chicken and used the leftover carcass to make nuggets. The kids happily scarfed them down, to his sad amazement.
Dara O'Briain mocked this one as well, talking about Gillian McKeith's tendency to show people a table covered in all the crap they shoveled down their throats over the course of the week - and noted that the looks on their faces tended to be a mixture of pride and lust.
Any piece of anti-tobacco propaganda where the smoker/chewer actually looks pretty hot with a cigarette in his or her mouth or while chewing. Especially when it emphasizes someone trying to look cool by smoking or accuses the Tobacco industry of glamorizing the use and then clearly identifies how they've played up tobacco usage to look cool, which the viewer may not have noticed before.
Drugs Are Bad. Anti-drug propaganda suffers heavily from this. Many works spend the first half detailing just how fabulous the wild and crazy world of drug-fueled parties are or throw in things like a funnystoner character or a Mushroom Samba. It's hard to take it seriously when they conclude with "Drugs are bad. You shouldn't do drugs."
Hilariously, there are multiple studies saying that anti-drug propaganda, both fictional works and real anti-drug programs, like DARE, not only fail to decrease the rate of drug and alcohol use among the participants, but in some places the rates actually increase. There are a couple of reasons as to why this is;
They expose kids to drugs at an earlier age. How many wouldn't even have known about these evil and destructive substances if they hadn't been told about them by the very propaganda trying to keep them off drugs?
It makes drug use seem far more prevalent than it actually is, making kids think it's normal, especially when they place emphasis on resisting peer pressure, which a lot of kids take as "everyone is doing drugs but you" and also "if you don't do them, prepare to be bullied and ostracised."
When the kids get older and find out that some of the information given to them had been, at the very least, exaggerated in order to Scare 'Em Straight, (e.g. one joint of marijuana or one pill of ecstasy will kill you) they assume that all of it was and decide to try out drugs. For the kids to discover this, all it takes is them knowing one person who uses or has used drugs and didn't die or become a desperate junkie.
Even when being honest, describing the effects doesn't exactly make them unappealing. "Marijuana makes you feel happy and makes things funny. LSD and mushrooms makes you see bright colors and patterns. PCP turns you into Superman."
The Aggressive Drug Dealer doesn't exist, so if a kid does get approached by a drug dealer, they won't feel nearly as much pressure to buy from them and will realize that real drug dealers, even if they aren't nice, are much nicer than the ones on TV and may feel more inclined to buy from them.
Some anti-drug programs even tell students the current street value of drugs. Which instead of resulting in "Oh, I would never do that that's too expensive" sometimes results in "Hey, *insert drug* is not badly priced."
Normal youth rebellion. Your parents and teachers don't want you to do this stuff, but they said that about all the good music, movies, and video games too.
In addition, pirating your DVDs is a good way to be freed from that annoying anti-piracy trailers.
And work around the region codes in a No Export for You situation. At least when you do not have to worry about a language barrier.
Video game DRM can get even worse - certain developers seem to take "aggressive DRM" to mean "everyone is a pirate, especially if they legally bought it" and nearly make their games entirely unplayable for non-pirates, to the point where people are willing to pirate a game they would have otherwise purchased, or even download a crack for a game they already legally bought, just to get around that nonsense.
And one of the same companies that are pushing anti-piracy also distributed file-sharing software, promoting the ability of the software to download copyrighted media illegally: 
It does not help their cause that a lot of the people involved in the anti-piracy side of things tend to do downright rotten things in order to try enforcing their viewpoint. For instance, trying to sue a young woman in need of an organ transplant for sharing a whopping ten songs, and support the creation of legal measures like SOPA. Far from raising public awareness, actions and tactics like these just make the anti-piracy groups look at best like they are over-reacting, at worst like they are money-grubbing jerks out to squeeze every dime they can get from both customers and artists.
The cameras step into the house of a teenage girl whose life was ended by pregnancy only to find that, somehow, her life goes on. It's harder to fear something with which you've become more familiar.
It doesn't help that most of the "struggling teen mothers" portrayed in many of these media are rich white girls who don't have to get jobs or miss out on school or social events to take care of their baby, and can often still get a guy (whether or not he's the father of their child) to go out with them. In a more meta sense, since these women have appeared on TV, they have a certain amount of fame they can leverage into speaking engagements, public appearances, and even endorsement deals, further making it seem more glamorous to outsiders.
There's almost inevitably - especially in documentary versions - a statement somewhere about how, at least in her own estimation, she's become twice the person she was and how it's really matured her, and how one just doesn't know what love is 'til one is a mother. Yeah, kids, don't do it!
Meta-wise, it's literally having the opposite effect on its audience; because of the recent focus on fame and recognition as being the most important value among teens and tweens, there have been instances of young teenagers who want to (or did) get pregnant because they think they will appear on television.
Anything against acquiring excessive material goods, whether it's discouraging greed or if it's anti-consumerism or anti-materialism, can easily fall into this. The story often has to show all the material things that people shouldn't be so greedy for, shouldn't waste their money on, or shouldn't define themselves by, and it's extremely difficult to portray these things without them looking cool. This goes double when the message is aimed at kids.
This happens a lot in Christmas works that try to reinforce the true meaning of the holiday; about family, about giving to the less fortunate, and how it's better to give than to receive, which is then undermined by showing all the awesome presents we shouldn't be so focused on getting. These also tend to end on Sweet and Sour Grapes, where the person is resigned to the fact that getting [awesome toy] isn't what makes a happy Christmas; only to receive it after all.
Body weight related issues, either getting too heavy or becoming too thin.
For example this ad warning about the dangers of anorexia shows a cadaverous-looking young woman◊ (Warning — NSFW image). However, while people without weight issues might be disgusted by sights like these (but it's not like they were going to suddenly become anorexic or obese anyway), they can also give grounds for denial: "I'm not anorexic/obese: I don't look like that!"
With weight loss in particular the works can become icons as a goal to reach, or for viewers/readers blaming themselves. "Look at her, I couldn't even go as far as she did!"
In the case of some who have gone through the experience of having an eating disorder and managed to "beat" it, a lot of times they used pictures like these as "thinspiration" and seeing those images may trigger a relapse.
Going the other way, fat/body positive messages that are supposed to tell people who are seen as "large" by society's standards but are actually at a decent, healthy weight that there is nothing wrong with them could be used by actual obese people as an excuse to keep living an unhealthy lifestyle.
Sex Is Evil. Works that make arguments against sex or portraying it openly, whether its discouraging sexual immorality and promoting abstinence or if it's arguing against the objectification of women.
The work inevitably has to show some sexual imagery, and it's pretty much impossible to show it in a non-appealing light, so it either the sex or the portrayal of women off as appealing.
With works that promote abstinence they often get screwed up by trying to balance out the message of how evil and dirty pre-marital sex is with how great and wonderful sex is once you're married. Unless the work resorts to outright lies, it really has no argument to show any differences between sex within marriage and sex outside of it other than, "It's bad/sinful/immoral".
A.) It's no coincidence that the virginity pledge movement and abstinence trends like purity rings have coincided with rising rates of oral and anal sex among teenagers. While individual leaders and parishes have given their opinions on oral and anal sex, the churches of each sect have yet to take an official position on them. Because oral and anal sex can't result in pregnancy, this leads kids to believe they're just a little bit less sinful than vaginal pre-martital sex, and that it doesn't technically count because it's not the same as vaginal sex.
B.) Even with vaginal sex, kids can still find other loopholes, such as being engaged or being "spiritually married". They're not actually married, but they believe that you can still do it as long as you get married later. That part's pretty much in the Bible: ancient Israelite (precursor to Jewish) law specified vaginal intercourse between a man and woman who were both unmarried as being exactly equivalent to marriage vows, the couple becomes instantly married (modern equivalent being "common law" marriage). Hence what seems to be a punishment for premarital sex (marriage) is actually a logical consequence (and hence no ban on fiancee sex).
Fewer half measures. Sure, total abstinence is a more reliable way to avoid pregnancy and STDs than using a condom, but using protection is way better than nothing. Programs that primarily preach abstinence tend to condemn protected sex as well, so when the kids give in to their lust they almost certainly won't already have a condom on them "just in case", may not know how to get and use one, and may be unaware of how effective it is and thus not think it's worth the trouble.
Tellingly, areas that largely utilize abstinence-only sexual education tend to have higher rates of teen pregnancy than places that instead use comprehensive sex education.
Along the same lines, prostitution is devilishly difficult to portray in film without glamorizing it. Sex Sells, after all, and it's difficult to show a hooker plying her trade without showing what some of the appeal of that trade is. At the same time, if you do succeed in making prostitution look unappealing (via perhaps showing the cruelty and perversion of the customers or maybe the dangers of the trade), you're very likely to make your film rather unappealing as well, and then no one wants to watch it.