Star Trek Canon Recs

ST:TOS Must See
1.14 Balance of Terror - introduces the Romulans
1.22 Space Seed - set the stage for STII
1.26 Errand of Mercy - cements Fed-Klingon relationships in the 23rd century
1.28 The City on the Edge of Forever - one of the highest fan-rated eps
2.1 Amok Time - introduces Vulcan; Spock gets dumped at the altar
2.4 Mirror, Mirror - introduces the Mirror Universe, revisited in DS9/VOY/ENT
2.10 Journey to Babel - introduces Spock's family (Sarek had his own following)
2.15 The Trouble With Tribbles - fluffy (literally!) & hilarious ep; revisited in DS9
3.10 Plato's Stepchildren - blah ep famous for historic first televised interracial kiss

ST:TOS Other Suggested Picks
1.15 Shore Leave - plenty of slashy subtext
1.16 Galileo Seven - great character growth ep for Spock
1.25 Devil in the Dark - introduces the popular Horta species
2.17 A Piece of the Action - fluff and crack
STII - fan favorite movie
STIV - my favorite movie
STVI - also fan favorite movie

( ST:TNG ep recs )

EDIT: Various images I came across on my way to choosing my icon.

http://www.wincustomize.com/explore/sound_schemes/38/
http://superherouniverse.com/articles/startrek.htm
http://www.fabuloussavers.com/stall014.shtml
http://johneaves.files.wordpress.com/2009/04/painting2.jpg
http://onlyhdwallpapers.com/wallpaper/uss_enterprise_star_trek_the_next_generation_desktop_1280x1024_wallpaper-42562.jpg