My hybrid is, first and foremost, an all-weather commuter. Bonus: long weekend uptempo rides for fun.
For the bike:
-fenders
-rear rack and bungee cord
-(bike came with kickstand and water bottle cages)
-seat bag with multitool, patch kit, spare tube, zip ties, some cash, Band-Aids and alcohol wipes, tube of sunblock
-frame-mounted pump
-lights, backup lights, frame lights, extra reflectors...light up the night like a Christmas tree
-U-lock; cable lock for weird places
-bar ends
-debating heated handlebars for this winter!
-optional: detachable rear basket rigged as dog carrier
For me:
-helmet
-helmet cover for cold and rain
-gloves (I prefer full-finger)
-water bottles
-appropriate clothes for various weather and ride types
-I ride in skater shoes (platform pedals)
-on rides, bring my cell phone for emergencies and pictures
For home:
-floor pump
-cleaning supplies (oil, lube, rags, etc)
-car rack; electrical tape around the clamps so they don't scratch
-a very understanding roommate
Are you wanting recommendations for specific brands? Or just a general idea of what accessories to accumulate?