There used to be a range of 24 blocks around players where hostile mobs could not spawn. This rule is still described in the wiki.
However I have on multiple occasions seen skeletons, creepers, spiders and zombies spawn within less than that. The latest creeper was at 5-6 blocks distance right when i'm looking in that direction.
Additionally they instead of immediately despawning once player is 128 blocks away, they remain frozen and are saved in the chunk. This is evident when you return to the location by day and skeletons/zombies start burning. This also applies to vertical distance. In 1.6 when I was 130+ blocks above ground i had no loaded entities, now they remain loaded and applied to mob caps.