Delphine always vanished during the fight at the bridge keep for me. I'd find her again at the dragon mound I was supposed to follow her to. On the third playthru I just went to Kinesgrove first then when I came to that quest I could just teleport to it.
My most buggy follower is Lydia. No matter what gear I give her she will not upgrade from her stock stuff.
My Lydia wears a steel-horned helmet now. I did get her to use some dwarven boots once, but I thought they looked terrible with the rest of her steel outfit, so I took them away. She can use a staff too, and has that lovely infinite-arrows thing that I find so useful. Just find a few daedric arrows, give them to her, and let her multiply them for you in some long archery duel with a camp legate, or someone else who can't die.
Aela will act weirdly during, er, a certain big quest.
She talks to you normally, but constantly runs away from you. If you stop chasing her, she'll be gone. That was quite annoying, but fortunately she was available again after the conclusion of this quest.