Two Kirks Are Better Than One
A well-known trademark in Star Trek is the ever-popular "make do with what little you have" philosophy. In other words, "Recycle everything you can since we ain't got no budget because the studios know Nielsen ratings and nothing else." Fans find this amusing ... not because it's a great idea, but rather because the producers thought they could pull this off and get away with it. Yeah, as if we're not going to notice. Everyone can tell when corners are cut.
One classic revolving theme: multiple copies of a main character. Let's take Kirk, our brave leader. The universe always wants to duplicate the Tiberius because of his greatness and he saves the galaxy every week.
"The Enemy Within" - this is an early favorite. Transporters are apparently sensitive around this period in Federation history and some weird ore screws things up enough to create opposite-duplicates. While this was never technically explained, this is almost akin to the holodeck creating real beings out of supposedly-fictional characters.

Garth of Izar in "Whom Gods Destroy" had the magical ability to change himself into whoever he wanted. The Captain, of course, is a logical choice since it would potentially put him in a very powerful position. It also gave Shatner a chance at more inspirational performances of his special blend of dramatic flair:

...not to mention the opportunity to bring in a stunt double who from the right angles is noticeably different from Shatner:

In "What Are Little Girls Made Of?" we realize why being human is so inconvenient - we have to eat to survive. Kirk gets cloned and the new double happily states that androids don't need to eat. The new Kirk is "programmed" by the real one which tips his half-breed first officer into realizing that something isn't right. Human ingenuity again saves the day. Yahoo.

Then in "The Undiscovered Country," Kirk's in trouble again with the Klingons. They're steaming mad and found a way to throw him and the good doctor in prison. Along the way, his jail-break partner morphs herself into a copy of him and another Kirk vs. Kirk ensues.

Of course, Trek wouldn't be Trek without spilling the same ideas over to a different series. Riker is the 24th century Kirk-equivalent ladies man, so naturally we're going to have an episode which duplicates him in "Second Chances" with the inevitable romantic complications. Due to another unintended transporter accident. Of course. What else could it be.

Tired of the transporters creating new beings out of thin air? Why don't we stick to the other over-used cliché : time-travel ... in the appropriately-named episode "Time Squared":

Apparently, nobody gets tired of episodes where they stamp out replicas, so let's do Picard again in "Allegiance" where aliens create a copy of him to command the Enterprise while they hold the real one in some observation lab.

The "holodeck episodes" were full of crew duplication, thanks to Mr. Barclay. But this whole "let's give one of the main cast a chance to play multiple roles" thing got out of hand in "A Fistful of Datas" where (once again) the holodeck goes berserk.

Brent Spiner was given a number of episodes like this, like where Data and Lore are seen together as well as in "Nemesis." One of these days, we'll just have to create a holodeck full of Cylon skin-jobs for the whole nine yards.

Oh, so you say you're sick of holodeck and transporter malfunctions to make an episode? Well, behind door number three we have our undisputable favorite - parallel universes! And for bonus points, we'll once again come up with an original episode name - "Parallels!"

I am so waiting for the movie where the brave crew does that slingshot-around-the-sun thing and goes back in time and somehow ends up in a parallel universe which happens to be a galaxy-size holodeck where everyone has to use the transporter to get back to their point of origin which inevitably creates a million duplicates of each person that leads to a universal disruption of the space-time continuum.
I'd like to see how they solve THAT problem.