There are a total of 8 companions, 6 humanoid and 2 non-humanoid. You can only have two in your party at once though, 1 humanoid and 1 non-humanoid. The following is a list of the companions.

Permanent Companions:

Humanoid:

• Arcade Israel Gannon, a member of the Followers of the Apocalypse in 2281 who can be found in Freeside's Old Mormon Fort.
• Craig Boone, a former NCR 1st Recon sniper with a grudge against Caesar's Legion and a chip on his shoulder. He can be found at night in the dinosaur at Novac. Can be recruited after completing One for My Baby and choosing particular dialogue.
• Lily Bowen, a friendly nightkin and former assassin in the Master's army. She can be recruited in Jacobstown after gaining the quest Guess Who I Saw Today.
• Raul Tejada, a ghoul mechanic and former gunslinger held hostage by Tabitha, the mad leader of the State of Utobitha. Can be found in Black Mountain.
• Rose of Sharon Cassidy (also known as Cass), a former caravan merchant and the daughter of John Cassidy. She can be found in Mojave Outpost.
• Veronica Santangelo, a disillusioned Brotherhood Scribe. She can be found at the 188 trading post.

Non-Humanoid:

• ED-E, a prototype eyebot designed for combat and reconnaissance operations. It can be found in Primm, in a non functional state, lying on the counter inside the Mojave Express, which is labeled in-game as "Nash Residence." ED-E requires 65 Repair (or 35 Repair if possessing a 55 Science skill) to fix it, or 3 pieces of scrap metal, 2 sensor modules, and some scrap electronics.
• Rex, is a cyberdog in Freeside under the ownership of the King. He is suffering from neural degradation as his old brain decays. He can be recruited after finishing Nothin' But a Hound Dog.