Indiana jones would flick his whip around the lid and fling the jar into the air, hitting a projecting stone which turns out to be a switch that activates an elaborate and ancient death trap that can only be escaped by the liberal use of jump cuts. The prehistoric whatever-it-is collapses into rubble, and Indy barely escapes with his hat, his whip, and his life. As he lies gasping in the dust, the jar rolls out of the ruin and fetches up at his side, where the lid drops off and pickle juice spills onto his leather jacket. Dr. Jones resignedly eats a pickle, and the audience chuckles.
Filthy assistants! Open this pickle jar for me!
–Spider Jerusalem
Doctor Who: Sonic screwdriver. Man, that thing can do anything.
Ash (Evil Dead/Army of Darkness): Blows jar apart with shotgun.
“Here are your pickles, Baby”
From the Whedonverse:
Buffy would stake the jar. Or kick the top off of it with her stylish yet affordable boots.
Angel would just kick it open as well but the pickle jar would be in front of a door which would be kicked down at the same time. Puppet Angel would not know what to do.
Malcolm Reynolds would just shoot the top off of the jar nonchalantly. “I open the jar, I eat the pickle.”
Jayne would intimidate the jar into opening by menacing it with a knife. He wouldn’t actually have to touch the jar in order to get it to open.
River would kill the jar… with her brain!
Niska would ask the jar “Are you solid?” at which point it would shatter in fear.
Any other Whedonverse fans feel free to chime in… we could go on all day with these…
Rorschach would pull off the lid with one hand in one twist, sheering off the glass “threading” on the neck.
The Punisher eats dehydrated pickles from an MRE, dry.
James Bond uses an electromagnet built into a lapel pin, intended to deflect the path of bullets, to open a pickle jar in the Q branch kitchen. "Honestly 007, do try and pay attention!"
Colossus/Guardian orders the jar to be opened, or they’ll vaporize the Vlassic Pickles headquarters with an atomic attack.
Wolverine would…carefully punch a hole in the lid with a canopener, drain the brine out in the sink, rinse out the jar and the pickles with bottled water, open the jar wearing rubber gloves, take out the pickle in the middle of the jar with tongs, then throw the jar and the rest of the pickles away. (Logan doesn’t like it talk about it, but he has really severe Obsessive-Compulsive Disorder.)
Judge Dredd would invoke the Security Of The City Act, declare pickles illegal, and go round busting the heads of any scumbags selling black-market pickles. Hell, he did it for coffee and sugar. And Umpty.
And succeed.
And suck seed. 
Bah. Heroes are overrated. What about the villains?
Media muckracker J. Jonah Jameson would declare the pickles public enemy number one while running front-page editorials like: UNOPENED PICKLE JARS: THREAT OR MENACE?
Dr. Emil Gargunza would study the pickle jar and then reverse-bioengineer its contents back to first principles using cloned cucumbers, vinegar and other arcane ingredients, and make his own marvelous pickles.
Mister Croup would attempt to alternately threaten, cajole and frighten the pickles out of the jar, much to his frustration. Mister Vandebar would simply devour the glass jar, enjoying the sensation as the glass shards sliced opened his cheeks as he chewed. The mad angel Islington would find himself unable to free the pickles and instead, enjoy a heady vintage of pickles from the drowned city of Atlantis from his own private stock.
Brainiac, having trapped the pickles in the jar in the first place, would refuse to restore them.
Magneto would be convinced the jar of pickles represented the finest of cucumber superior and would insist on a separate shelf in the kitchen, away from the other canned foods.
Dr. Doom would devote all his power, all his arcane studies, to find a way to free his mother’s pickles from bondage.
Lex Luthor would would use his duplicator ray on the jar and accidentally create a bunch of pasty-white, chalky imperfect pickle duplicates whose motto would be to do everything the opposite of Earth-pickles.
The Beagle Boys would hatch some sort of unlikely scheme that, like their raids on Uncle Scrooge’s vault, would result in predictable failure.
The Anal-Retentive Killing Machine?
John Constantine would get Chas to open the pickles for him. “C’mon, you owe me, mate.”
(Reading Discworld right now) I’m picturing Rincewind picking up the pickle jar when he hears a voice next to him. “WOULD YOU LIKE A PICKLE? IT WON’T HURT.” He thinks better of having a pickle.
Han Solo would use the hydro spanners.
Q would just alter reality such that the jar was already opened.
Vash the Stampede doesn’t like pickles.
Homer would get Marge to do it. (Hey, Homer’s a superhero to some of us!!)
The Crimson Chin would use his chintastic powers
and the Tick would use a SPOOOOOOOOOON!
Askia, I hate to raise grammatical points, but the first mention of the Beagle Boys in any article, story, or column should be followed by the parenthetical “The Terrible Beagle Boys!”
Starman would probably launch into an interior monologue about how cool pickle jars looked back in the early '60s, and how a lot of those are collectible now.
Blue Beetle would get frustrated trying to open the jar, have a few Twinkies instead, and then feel really bad about himself.
Jesse Custer would ponder using “the Word” to make someone else open it for him, but he would open it himself because that’s what real men like his father and John Wayne would have done.
Jack Marlowe, CEO of the Halo Corporation, would teleport the pickles out of the jar, or perhaps he wouldn’t even bother because he doesn’t need to eat.
Tao would manipulate his Prodigals into competing with each other to be the first one to open it for him, and at least somebody would end up dead.
Jack Bauer would ask for a hacksaw.
Frodo and Sam, with great difficulty, would eventually throw the pickle jar into the Cracks of Doom. The heat would crack the glass, and the fried pickles would be distributed amongst the hobbits and sundry in celebration.
Jet Li, as the Prefect, would tell an intricate – and beautifully filmed – story about how he dueled with the pickle jar in his mind. Emperor Qin would figure out that telling this story was the only way the Prefect would be allowed within 10 paces of Qin’s pickle jars.
And the Q of 007 fame would use a rapid-fire version of a 1920’s Style Death Ray, cleverly concealed in his brolly, to melt the glass of the jar, thus freeing and ruining the pickles.
Quoth Q:
Ford Prefect would become frustrated by the fact that his entry on how to open a pickle jar had been edited down to only one word: Turn.
Arthur would be completely flummoxed by any attempt to open the jar, and whine about how he’d rather have some tea.
Zaphod would have no trouble at all, what with the three arms and all.
Trillian would calculate the exact trajectory and amount of force needed to turn the lid. Strangely enough, this would be exactly the amount of force needed to turn the wheel of one’s moped when going around Hyde Park corner.
Marvin would sulk about how he has a brain the size of a planet, and here he is, asked to open this jar of pickles. Life. Don’t talk to me about life.
Benji and Frankie Mouse would simply hire Slartibartfast to do it for them.
Slartibartfast would become lost in admiration of the little crinkly bits around the lid’s edge.
The mattress would just flollop.
The jar of pickles itself, however, would simply think “Oh no… not again.”
Bender would give the Jar of Pickles to Fry and go find a bottle of beer instead.
Akane would give the jar of Pickles to Ranma to open them, Ryoga would feel the need to open them to prove his love to Akane and would splash water on Ranma, turning him into Girl type Ranma. Girl type Ranma wouldn’t be able to open the Jar, and would start fighting with Ryoga. Kuno would come along and see The pig-tailed girl and Akane, and would immediately want to open the jar of pickles, but Shampoo would stop him, and say that Jar of Pickles is Ranma’s, Moose would intervene, and all hell would ensue. Eventually Genma would come along and eat the entire Jar of pickles, and the whole group would chase him down the road.
Oh, and Sampson would have no problem opening the Jar of Pickles, but The Monarch will attack and he will be busy fighting henchmen. Hank and Dean will see this as a chance for adventure and will run off with the pickles. After some Calamaty, Dr. Byron Orpheus will use his dark necromancer powers to open the Jar of pickles.