The most common thread I see is Dadmight, obviously. Mentor All Might struggling with the reality that he's basically given this scrawny kid a death sentence with One For All, then having to deal with the emotional fallout of watching that kid nearly destroy himself over and over. It's not just fluffy found family stuff either—some of the best fics dig into the guilt. Like, All Might retired, he's supposed to be done, but now he's having nightmares about young Midoriya ending up just like him, hollowed out and alone.
A surprising amount explore time travel or dimension travel. Midoriya ends up in a world where All Might died earlier, or All Might wakes up decades in the past with all his future knowledge and has to prevent his own mistakes. Those get weirdly philosophical about legacy and inevitability. There's also a subset that's pure hurt/comfort, where All Might finds Midoriya after a villain attack or a bad day at school and just... sits with him. No grand speeches, just quiet presence. It hits different than other pairings because the power imbalance is so baked into their canon relationship—exploring the shift from symbol to person feels huge.
Occasionally you'll find darker AUs where All Might is the villain, or Midoriya turns villain and All Might has to face him. They're rare but memorable when done right, usually focusing on the tragedy of the disciple surpassing the master in the worst way possible.