Think my favorite episode would be from DS9 "Trials and Tribble-ations" where for the 30th anniversary of Star Trek the cast from DS9 travel back in time to the original Star Trek.

It's definitely very hard to pick a favorite out of all 4 series (I refuse to count the abortion that was "Enterprise").

If forced to pick one I would probably go for "Trouble with Tribbles" from TOS.  It is absolutely flawless.  From TOS I'd say the following were my top few with roughly equal weight

    "Squire of Gothos", "A Taste of Armageddon", "Errand of Mercy", "Space Seed", "City on the Edge of Forever", "The Changeling", "I, Mudd", "A Piece of the Action", "Trouble with Tribbles", "Let that be your Last Battlefield", "For the World is Hollow and I have Touched the Sky"

(obviously I'm having a hard time narrowing it down)

Out of TNG alone I'd probably go with "Cause and Effect".  To me that is the quintessential Star Trek episode.  I also really love "Ship in a Bottle".

It's also kind of amusing to think of the WORST TNG episodes because it is absolutely astounding that they coexist in the same series as so many great episodes.  Without a doubt, the worst 3, standing in a pantheon of crap worthy of "Star Trek: Enterprise" are "The Child", "Cost of Living" and "Sub Rosa".  It's quite a thing to contemplate: "Sub Rosa" (in which Crusher is seduced by a guy who lives in some sort of lamp) and "Cause and Effect" were from the same TV series.  Amazing really.

As much as I liked both DS9 and Voyager I don't think they are quite in the same league as TOS and TNG.  DS9 had some wonderfully unorthodox episodes like "In the Cards".  Voyager I think was the most consistent of all 4 series, with some more formulaic goodies like "Scorpion".    Who can forget how Jeri Ryan manages to be one of the most gorgeous women anybody has ever seen and yet still play so stoic a part so well?  It's oxy-moronic really.

For best movie, without a doubt I say "Star Trek VI: The Undiscovered Country".  The cast is in a rather geriatric zone at that point, but it really doesn't matter.

I always found Voyage to be the worst of Star Trek series, Enterprise was starting to get interesting when they canned it. That two part episode " In a Mirror Darkly " is a brilliant take on the classic series "Mirror Mirror". 

I would also say that the best of the classic Star Trek Films are Undiscovered country and the Wrath of Kan. 

I have no favorites from all series but from TNG:

TNG: The Inner light.

http://en.memory-alpha.org/wiki/The_Inner_Light_(episode)

Brought me to tears. A wonderful episode.

I did kinda like DS9's "The way of the Warrior", but then again I was given that episode on VHS for my 18th birthday, lol.

TOS : The Trouble with Tribbles.  What can I say about this one - the only guy to wear a red shirt and survive picks a fight with a pack of Klingons just because they poke fun at the Enterprise.  The Klingons shoulda known better.

TNG : For me it's kind of hard to pick out any specific episodes (I know that I missed quite a few of them on TV) so I'm going to do a cop-out and pick the movie, First Contact

DS9 : As I said above, The way of the Warrior.

Voyager : Like TNG, there's a lot of episodes I missed out on, but "The Raven" did have a lot of character development for Seven of Nine (still to this day the sexiest character ever to grace Star Trek)

Enterprise : The 2-parter mirror universe episode was almost certainly the best one.  The Borg episode "Regeneration" was better than most, but did ignore quite a few things that had already been established.