Ok Lets just say for whatever reason, Jedis as you know them turned up in the Star Wars universe. Maybe Q finds out about them, while viewing the different universes, and figures how interesting these beings are. Then POOF he moves a few into The Trek Universe, right before the time of 1st contact on Earth. He takes 5 random human Jedis from the Clone Wars, right before they are killed in battle, and drops them in right when the TNG crew beams out, and Cochrane is about to meet the Vulcans.

By doing this move, Q has infected the Universe with the Force, and other worlds gain a few force infused people. Along with a few governments like:

The Klingon Empire

The Romulan Star Empire

The Ferengi Alliance

The Cardassian Union

note: Things will still go forward like before, but now you have the Jedis in the mix of things. How do you see Trek History moving forward with this one change in the timeline?

Massive deaths until Mc Coy finds a way to treat "midichlorian infestation"

Kai Winn uses her Sith powers to cut Benjamin Sisko in half with a red lightsaber. Then she electrocutes Odo to death with lightning.

Then she mounts a huge death laser on DS9 and goes out to conquer the known galaxy. My god this story arc would have been SO much better!

Geez I forgot to add a few people on Earth would gain Force power, and the 5 Jedis would teach them the ways of the force. So that would give them a leg up on everyone else. hehe.

The Benjamin Sisko thing kamiyama317 is talking about, wouldn't happen that easy if you had Jedis Serving in the Federation. lol

Jedi would not be allowed in starfleet

they would be hunted down and sent for medical treatment (Jedi powers are caused by a parasite)

Yeah..., just like they found a DNA Enhanced Dr. Bashir at a very young age and fixed him...

Oh wait...

had bashir been caught and fixed many lives would have been saved

the same with Khan had he been fixed there would have been no problem

Wait Dr Bashir was a murderer? I didn't know that... and I watched the series.

oh yes
Bashir had blood on his hands
(watch it again you then have an excuse to check out Kira and Dax)

Well, if the USS Enterprise E is still in orbit, the sensors officer will detect the entities from another universe. Due to the fact that they just got done fighting borg, it is highly likely they would be looking for any more of these anomalies. Therefore, the crew would abort the time warp to investigate. Upon learning of Q's actions, Picard will be very displeased (to say the least...) With no other choice, the timeline has now been altered, Picard would beam the Jedi into the brig and go back to the present, preventing any further timeline contamination.

The Star Trek universe does not contain any midichlorians. Assuming the USS Enterprise's transporters don't screen them out as a pathogen, they will spread. It is also possible for them to have spread in the past with that brief contact on Earth. The Force is unusable until the midichlorians spread far enough. Upon learning of the spreading midichlorians each race will react differently.

The Klingon Empire will fear it and treat it like a plague. Think about it, the force allows for deception (through mind tricks), telekinetic powers, and increased agility. The first trait alone will enrage the Klingons. They will attempt to "cure" it by working on a device that destroys it or nullifies it.

The Romulan Star Empire will study the force and attempt to adapt it for their own purposes. The Tal Shiar will experiment and test it in their espionage tactics. If it is found to be viable, it is likely they will adapt it for all of their missions.

The Ferengi Alliance...yeah...we all know what they would do with it. A biological entity that allows them to read their customers minds? I see every Ferengi in the galaxy lining up to obtain the force.

The Cardassians will use the force to obtain information from captives. It is likely they will mainly use it for torture and confusing the minds of their prisoners.

The Federation will view the force as a sentient lifeform and attempt to get the Jedi back to their universe. Assuming Q is willing to help (he probably won't simply because he is enjoying himself), then Q will simply revert everything he did. Now if Q isn't willing to help...Starfleet will call Sisco to "persuade" him. A few punches to the face later, Q decides the whole thing isn't fun anymore, so he reverts everything.