Fallout 1: Really the biggest challenge was keeping any of them alive for a long period of time. Tycho was probably the most resilient since he came with leather armor and a hunting rifle, but it wasn’t immediately obvious how to recruit him.
I actually managed to keep all recruitable companions alive right up until I had to face the Lieutenant, at which point one of his buddies wasted all of them except Katja (Who was the most useless out of the recruits!) with a rocket launcher.
I suppose Dogmeat was the most reliable though.
Fallout 2: You were pretty spoiled for choice in this one and walking around with a personal army consisting of ghouls, super mutants, robots and deathclaws was pretty cool.
But for me, the one that tended to be the most reliable and I never had to baby sit was Vic the Trader. Give him a good gun and usually never missed. I know most liked Cassidy, but I always found that Cassidy was a bullet magnet for the enemies or he’d often position himself in such a way that he was bound to get shot a lot, even when I told him to stand back.
Either way he always died a lot when I recruited him, so Vic tended to be a better choice when it came to “normal” companions in that game.
Fallout 3: Charon was probably the only useful one that was willing to travel with me. Dogmeat always died fairly quickly.
Fallout New Vegas: ED-E for most of the way, though I usually had Boone with me too except when I did a Legion run through once. Usually hired all of them at some point for various missions though (Veronica to enter the BOS with ease, Arcade to get the Enclave’s help, etc)
I actually liked all the companions to some degree in this one, but the main problem was you usually got ED-E and Boone first, and when you got those two, you never really needed anyone else. Plus the other ones typically came a lot later in the game when you didn't really need the extra guns anymore.
Fallout 4: Dogmeat, but that’s mainly because you still get the Lone Wanderer perk when traveling with him and he’s not judging you ever five seconds. This set of companions are some of the biggest whiners yet, seriously, even the Super Mutant is a big whiner! If I wanted companions that scolded me for my actions every other choice I’d go play a Bioware game.
Though Nick's 1940 detective persona makes him pretty entertaining to travel with most of the time.