A (Mostly) Complete List of Ways to Obtain Creature Companions in Pathfinder First Edition:
(Sourced from this thread: https://paizo.com/threads/rzs2pjan?Ways-to-gain-a-Familiar-or-Animal-Companion)
Animal Companion/Mount options:
• Barbarian: Mounted Fury (5th; bestial mount; -4; APG) 
• Barbarian: Mad Dog (1st; war beast; Animal Archive) 
• Cleric (4th; animal domain; -3) 
• Druid (4th; nature bond: animal domain; -3) 
• Druid (1st; nature bond: animal companion) 
• Druid: Treesinger (1st; plant bond: plant companion; ARG) 
• Druid: Pack Lord (1st; animal companion; UM) 
• Paladin (5th; divine bond: steed) 
• Ranger (4th; hunter's bond: animal companion; -3) 
• Ranger: Beast Master (4th; animal companion; -3 until 12th; APG) 
• Sorcerer: Wildblooded (4th; sylvan bloodline: animal companion; -3; UM)
• Cavalier (1st; mount; APG) 
• Cavalier: Beast Rider (1st; exotic mount; UC) 
• Cavalier: Huntmaster (1st; hunting pack; Animal Archive) 
• Inquisitor (4th; animal domain; -3; APG) 
• Oracle (1st; nature mystery: bonded mount; APG) 
• Samurai (1st; mount; UC)
Familiar options:
• Bard: Sea Singer (2nd; familiar; APG) 
• Cleric: Demonic Apostle (drow; 1st; demonic familiar; ARG) 
• Cleric: Fiendish Vessel (tiefling; 3rd; fiendish familiar; ARG) 
• Druid: Blight Druid (1st; nature bond: familiar; APG) 
• Druid (1st; eagle domain; UM) 
• Druid (1st; toad domain; UM) 
• Druid (1st; monkey domain; UM) 
• Druid (1st; serpent domain; UM) 
• Rogue (10th; advanced rogue talent: familiar; -4; UC) 
• Rogue: Carnivalist (1st; familiar; Animal Archive) 
• Sorcerer (1st; arcane bloodline: familiar) 
• Sorcerer (3rd; serpentine bloodline: serpentfriend; -2; APG) 
• Wizard (1st; arcane bond: familiar)
• Alchemist (2nd; discovery: tumor familiar; UM) 
• Gunslinger: Buccaneer (human; 1st; exotic pet; 1/2; ARG) 
• Magus (3rd; magus arcana: familiar; UM) 
• Ninja (10th; master trick: advanced rogue talent: familiar; -4; UC) 
• Witch (1st; witch's familiar; APG) 
• Witch: Beast-Bonded (4th; enhanced familiar: +1 to effective witch level; UM)
Other:
• Anti-Paladin (5th; fiendish boon: fiendish servant; APG) 
• Summoner (1st; eidolon; APG) 
• Summoner: Broodmaster (1st; eidolon brood; UC) 
• Summoner: Master Summoner (1st; lesser eidolon; UC) 
• Summoner: Synthesist (1st; fused eidolon; UC)
Feats that improve effective levels (bonuses capped by HD):
Beast Rider (half-orc; +2 to effective druid level; ARG) 
Boon Companion (+4 to effective druid/wizard level; Animal Archive) 
Huntmaster (human; +1 to effective druid level; ARG)
