One Piece's Monkey D. Luffy is so suggestible that the hypnotism doesn't even have to be aimed at him. He was hypnotized by a chakram on a string from over a hundred feet away, when the guy doing the hypnotizing was trying to hypnotize his underlings, not Luffy, and was surrounded by so many people that Luffy should barely have been able to see the chakram, let alone concentrate on it hard enough to be hypnotized.
This is especially interesting when you realize that he's a Determinator with one of the strongest wills and most stubborn mindsets in the series. He's just really easily hypnotized. Of course, he's also the quintessential Idiot Hero, and the Rule of Funny always applies. Of course that hypnosis made him much, much stronger. So maybe he wanted to take advantage of the enemies' techniques. Or, he really is that suggestible, considering earlier he fell asleep just by looking at the chakram. Also notable is that the first hypnotist we see in the series is almost as susceptible to his own hypnotism powers as Luffy is.
Later subverted, when his stolen shadow resists the villain's control for quite a long time, while normal people's succumb instantly and all of his comrades only resist on some very strict principles they have, being submissive otherwise.
Gilbert from Pandora Hearts has been brainwashed multiple times as a kid, as a grown up and in his past life. It's a wonder how he's able to keep Oz alive.
Wolfram from Kyo Kara Maoh! is subjected to this. Justified though because the key to unlocking the greatest evil in the demon world is his heart and as the series goes on and the seal to the great evil weakens, he starts zoning out more often than not.
Superman has a rather undeserved reputation as this, due to the frequency with which people brainwash him. It's not as though he's exactly weak-willed, and in fact often breaks out or at least partially resists their control himself. It's just that he's such an attractive target for brainwashing that it happens a lot. And it's also one of the few holes in his otherwise-invulnerable powers. While he's not weak-willed, his lack of any special protection against mind-control or magic makes it seem like a glaring weakness compared to his other capabilities (and, well, relatively speaking, it is).
Despite her very strong personality, Lois Lane is surprisingly vunerable to hypnosis, at least in the Golden Age, with a tendency to fall very quickly and very easily into a trance. In 1940/41 alone she was hypnotized in five different stories.
The Squadron Supreme, a Captain Ersatz of the Justice League who existed to job to Marvel heroes, were retconned to be Weak Willed due to their universe's absence of mind-controllers, in order to justify the way they were mind-controlled in every single one of their encounters with the mainstream Marvel heroes.
Donald Duck in the comics is prone to boasting he's immune to hypnosis and subsequently being extremely easily hypnotized. In one story by Carl Barks he was even hypnotized by a children's toy he only imagined to have the power to do so. In another by Don Rosa, he fell asleep immediately as soon as the hypnotist started speaking about sleepiness.
Actually used as an advantage in an issue of Justice League Europe in which The Flash (Wally West) is the weakest-willed member of the team, and therefore he's the only one who's able to pick up an extremely weak telepathic distress call from another dimension.
Films — Live-Action
Star Wars: The original Jedi Mind Trick only works on "the weak-minded". This means sometimes it works and sometimes you're going to hear "mind tricks don't work on me — only money."
In one of the Abbott and Costello films, a psychologist tries to hypnotize Lou Costello. Lou proves to be completely immune, but the psychologist accidentally hypnotizes himself. Then Lou wakes him up, and managed to accidentally hypnotizes him again mere seconds later.
Mina Harker in Francis Ford Coppola's Dracula. It seems all you have to do is wave your hand in front of her face and she's in a trance.
The entire Cavewight race has this problem in the Chronicles Of Thomas Covenant. Combined with the fact that they're physically large and powerful, this got them warped by the Big Bad from a race of peaceful miners into his Ax-Crazy shock troops.
The Imperius Curse works this way; it will enslave weak-willed to do the caster's bidding. In this case, however, it also depends on the intention behind the caster, because if they don't mean it, it will be easier to break the curse. It's probably more accurate to say that it affects anyone who's not strong-willed; Harry was the only one out of his entire class able to throw it off (with difficulty).
Ron falls under this trope — he seems to fall under Veela magic more easily than the average guy (even a quarter-Veela is enough to affect him), was the easiest for Voldemort's locket to manipulate, and when Imperiused by Moody was actually still partially affected at the end of class (he couldn't stop skipping for a while). A Cheering Charm is known to cause the victim to break into a laughing fit when overdone, but it should be taken into consideration that the said victim was him.
Artemis Fowl is mesmerized more easily and more frequently than any other character in the series. It is not completely clear whether this is really a case of this trope; the only human known to have even partially resisted the mesmer is Butler, who is extremely strong-willed by anyone's standards. Also, while Artemis usually outmanoeuvres enemies rather than beating them through sheer force of personality, he does show great self-control and strength of character on other occasions. Also, he never tries to resist. It isn't physically good for your brain to, so he either plans to eliminate the possibility of being mesmerized or accepts that he will be and plans around it.
In The Dick Van Dyke Show Rob was hypnotized into acting drunk when he heard a bell; but the subject of the hypnosis was Buddy, not Rob, and he wasn't even in the room when the hypnosis happened.
Star Trek: Voyager ("Spirit Folk"). The Doctor is being held prisoner by the inhabitants of a holodeck program left on too long, and were weirded out by the crew coming and going like ghosts. To get some answers, someone suggests they try hypnosis on him. Being an A.I. Hologram himself, he dismisses it as childish... and he promptly gets completely hypnotized. Not to mention how he's reprogrammed into becoming evil at the push of a button in "Equinox".
Sarah Jane Smith may be one of the Doctor's most independent companions, but she's also been hypnotized or brainwashed more often than any of them.
Not as much as Amy Pond, though.
Morgana in Merlin is easily hypnotized or entranced.
Hicks from Alphas has a terrible track record when it comes to mind manipulation, starting in the first episode. In one episode he uses this to his advantage by having Nina brainwash him into believing he had switched sides. This gets progressively worse through the episode as he has his mind read (painfully), he gets talked into suicide by another Alpha, and then Nina talks him out of suicide by brainwashing him again into forgetting it.
Xander: Okay. Let's do this. *assumes boxing stance* No poofing. Come on puffy shirt, pucker on up 'cause you can kiss your a...
Xander: Yes master.
The Will Save of Dungeons & Dragons 3rd Edition (and to a lesser extent, its descendant, Will Defense, inf 4th Edition) dictates whether or not a character is Weak-Willed. It's based on the Wisdom stat and a class may or may not get a bonus to it. This lead to classes that prioritized Wisdom and with a good bonus (Monk, Cleric, etc.) to being very strong willed, while classes that prioritizes other stats and gave no class bonus (Fighter and Rogue, especially) being almost legendarily prone to this trope. A very real possibility is for the party's Min-Maxed warrior to turn on the party's Squishy Wizard the moment an enemy cast Dominate Person. Barbarians actually get a bonus to Will Save while raging to try and prevent just such a scenario.
The Star Wars d20 Roleplaying Game uses an identical mechanic — a character with a low Wisdom score is vunerable to a Jedi Mind Trick. Notably the rules state outright that Twi'lek's tend to be weaker-willed on average than humans (in game terms they have a Wisdom penalty). Hutts on the other hand have a Wisdom bonus reflecting their strong willpower.
Kain from Final Fantasy IV has built up a bad reputation due to the apparent ease his enemies have in brainwashing him to do evil. It actually only happened once — with a gap in the middle of the story where the signal was bad. Subverted in the end of the game, as evidenced by the "Read the lead member's mind" thing you can do in the DS version, where Zemus, the guy who controlled Golbez into mind-controlling Kain in the first place, so therefore better at mind control tries to control him again, this time by making him hate Rosa for choosing Cecil. He fights it off with ease.
In Final Fantasy IV: The After Years, it's Cecil, not Kain, who gets brainwashed by the Mysterious Girl. You do end up fighting Kain as an enemy a lot in the base chapters, all the time claiming he's not being controlled this time. He isn't. It's actually his dark side, given form and teaming up with the Mysterious Girl, just so that he can kill Cecil.
In The Order of the Stick, Belkar has a habit of succumbing to almost any enemy that tries to mind-control him. This ties into the Dungeons & Dragons example above, as Belkar is a ranger/barbarian and both classes have poor Will saves. Additionally, Belkar has such a poor Wisdom score he can't even use the spells he should get as a ranger, making his Will saves even worse.
Todd Apparently they have power over the phenomenally weak-minded.
And then they break the control just by shaking him a bit and saying "Snap out of it!"
The Nostalgia Critic has a rather worrying tendency to get manipulated and controlled really easily. For example, he would have done anything Sage as the Devil told him to do if it meant getting his mind erased of Sequel Month.
Homer on The Simpsons. One episode has him er... "resist" the most powerful mind control techniques of a commune, until they change the lyrics to the 1960's Batman score from "Batman" to "Leader".
The Transformers Animated version of Wreck-Gar doesn't even need to be hypnotized first. If you tell him something, he will do it. If you tell him he is something, he will believe it whole-heartedly, until somebody else tells him he is something else. This is mitigated — somewhat — at the end of his first appearance... when it is suggested to him that he be less suggestible.
Beast Boy, as shown in the page pic. He isn't a total pushover, but for some reason is really suggestible to Mad Mod's swirly TV screens. Must be because he is the dullest of the five, as well as some deep-rooted inferiority issues due to his relationship with his father figure, Mento. Or possibly just because they're on TV screens.
His one-time girlfriend Terra too, who relies on others to make choices for her, even if it's the evil Slade. Appropriately enough, Beast Boy manages to man up himself and get her to strengthen her willpower too, which leads to her redemption.
The Secret Show: Wanting to be called back into active duty, retired U.Z.Z. Agent Zach Meadows impersonated Dr. Hypno, a criminal from his days who hypnotized his actually her, but that wasn't revealed until the end of the episode where they appeared victims and he was the only one who managed to defeat her. Once he was exposed, he explained he could only affect people with low intelligence, which explains only Victor being affected. Unfortunately, the real Dr. Hypno didn't like being impersonated and came back from retirement to settle a score with the imposter.