You know I love Deep Space Nine. Not everyone has the time to invest in a new show, and DS9 has a rough introduction. To help some people get into it, I've compiled a list of five episodes from each season of Deep Space Nine that focus on essential stories and character moments of the series. I've also added a few supplemental episodes that are very good, but don't quite make the cut.
The Search, Part I (3x01): Meet Defiant, Starfleet's first warship. You'll have to watch the second part on your own time. ;)
Supplemental: Civil Defense (3x07): Just good times with DS9 itself and Dukat being Dukat.
Life Support (3x13): Bajoran politics. And Kira's relationship thing moves along. Pretty Star Trekky and still good somehow.
Supplemental: Heart of Stone (3x14): God! So much Odo!
Improbable Cause (3x20): Equal amounts of Garak, plus some Odo. This, The Wire, and By Inferno's Light/In Purgatory's Shadow are probably the essential Garak episodes. It also tells you a lot about Odo while furthering the main storyline.
Shakaar (3x24): Bajoran politics. This is really the last gasp of Bajoran rebellion storylines. While Memory Alpha doesn't back me up on this, at some point in the series, it stops being the "Provisional Bajoran Government" and just becomes the "Bajoran Government."
Supplemental: Facets (3x25): A Dax episode that lets the actors stretch their legs. It also has heapin' helpings of Odo.
The Adversary (3x26): Odooooooooooooooo.