I know several people who get by just fine with no addons at all, so them being a must have is largely a personal choice
Some of the more common/widely used addons are
master merchant
inventory insight
FTC or LUI or AUI
Combat Metrics
Advanced Filters
Wykkyd's Suite
Alpha Gear
Stormproof: Vibeke - 50 EP mDragonknight | Savi Dreloth - 50 EP Magsorc | Sadi Dreloth - 50 EP Magblade | Sigtric Stormaxe - 50 EP Stamsorc | Valora Dreloth - 50 EP Magplar | Sigtric the Unbearable 50 EP Stam Warden Scrub: Chews-on-Beavers - 50 EP DK Tank | Vera the Wild - 50 EP magicka Warden | Sigtric the Axe - 50 EP Dragonknight Crafter | Sigtric the Blade - 50 EP Lost Nightblade | Sigtric the Savage - 50 EP magicka Templar | Vibeka Shadowblade - 50 Ep Stealthy Ganky Nightblade |
A list of some good ones, along with descriptions of what they do. The 2nd tab has instructions for increasing LUA memory - which is something you'll definitely want to do if you start using addons as the game only uses 64MB for it by default.