I'm pretty damn far into the campaign, and I haven't run into a single companion. Are there any quests I should seek out that would lead me to some friends? 
 
Oh God. I'm so lonely.

Do the king's quests, that town with the dinosaur... I mean can't you just look it up? It should be really easy info to find.  
 
edit: derp

It's kinda of hard to miss Boone & Veronica  "so long as your pay intention talk to everyone before moving on"
 
ED-E is in Primm at the post office 
 
You will need a speech or barter of 50 or higher if I recall but you need to be on "the quest" you get later on for the crimson caravan co. to ultimately get this companion just to let you know in advance
 
There are others but I won't spoil but anyway those are the easy ones to get or can't miss!

I got some random Veronica bitch that follows me around. She doesn't do too much so you're not missing out.

Veronica is at the 188 Trading Post. 
Boone can be found in the head of the Dinosaur in Novac after 9PM. You have to complete a mission for him before he can be your companion. 
Rex is at the King's School of Impersonation. 
Cass is at the bar at the Mohave Outpost. You've probably walked right by her already during an earlier mission.
Other places to find companions are Jacobstown, Black Mountain & the Old Mormon Fort.

" I got some random Veronica bitch that follows me around. She doesn't do too much so you're not missing out. "

I got Boone pretty easily. He's a badass. I love it when he snipes dudes to death before I even get a chance to get a bead on them.

Get your ass to Jacobstown now.  Actually, come to think of it, I like most of the companions.