Here are my favorites:
Social Psychology Season 1, Episode 4. I really like Shirley/Jeff scenes - and there generally aren't enough of them on the series in my opinion. Plus, this one includes making fun of Vaughn, Britta's boyfriend at the time and a recurring Glendale character.
Contemporary American Poultry Season 1, Episode 21. A plan to bring chicken fingers back to the cafeteria, in the style of a mobster movie.
Modern Warfare Season 1, Episode 23. The first paintball episode (yes, there have been multiple). Also, Jeff + Britta sexual tension.
Epidemiology Season 2, Episode 6. Contaminated meat from the Army at a Halloween party results in everyone becoming zombies except Troy ("the first black man to make it to the end"). Some unexpected plot developments...
Cooperative Calligraphy Season 2, Episode 8. The 'bottle' episode, referring to an episode of television with only the regular cast usually in one room for the duration. This one is over who stole Annie's pen.
Abed's Uncontrollable Christmas Season 2, Episode 11. Shot in the claymation style of classics like Rudolph. Need I say more?
Critical Film Studies Season 2, Episode 19. A tribute to Pulp Fiction, and more importantly, a Cougartown cameo. (Fact: Abed really did appear on an episode of the show as a extra)
Horror Fiction in Seven Spooky Steps Season 3, Episode 5. Britta has the group tell scary stories to figure out which one is a psycho. Hilarity ensues.
Regional Holiday Music Season 3, Episode 10. A holiday-themed spoof of Glee. I would buy this soundtrack.
Paradigms of Human Memory Season 2, Episode 21. The classic 'clip show' episode - but unlike the cop-out episodes it mimics, all the footage is completely brand new.
Remedial Chaos Theory Season 3, Episode 3. Widely regarded as one of the best episodes of Community (maybe even television), the episode takes place at a housewarming party for Troy and Abed, with the group (unknowingly) experiencing different 'timelines' with the roll of a dice. A little repetitive, a little confusing... and completely awesome.
Foosball and Nocturnal Vigilantism Season 3, Episode 9. Most importantly, Abed does his spot-on Christian Bale as Batman impression. And we get some great Shirley and Jeff bonding over a foosball game against Nick Kroll (Fact: the foosball storyline returns in Season 4, Episode 4, but alas, Kroll does not. It's a shame, really.)
Pillows and Blankets Season 3, Episode 14. A spoof on a Ken Burns documentary, the episode features stunning photography by Britta during a pillow fort vs blanket fort disagreement between Troy and Abed.
Basic Lupine Urology Season 3, Episode 17. This time Community spoofs Law & Order and it is seriously spot on. The music, the acting, the roles of the different characters; also brings back
Intro to Felt Surrogacy Season 4, Episode 9. The one and only episode I'll include from the most recent season, and only because there are puppets involved.
And spend some time YouTubing post-credits scenes.
Honestly, in trying to put this list together I worried that there wasn't enough Leonard or Star Burns or John Oliver or the Dean or John Goodman as the dean of the AC Repair School or Magnum (POP POP!'). You might as well just watch the whole series.