Spider-Man's titles have gotten too confusing lately with the Other, Iron Spider shit, his apprenticeship to Iron Man, unmasking, etc. but I was thinking maybe Gravity being Spider-Man's apprentice would be kind of neat. Not a sidekick, per se, and not appearing in every issue, but Spider-Man really knows the ropes, a few scenes having him and Gravity patrolling, Spider-Man telling him about the various rogues active at any given time, the best procedures for certain situations, how to deal with the media, etc.
Or if he signs up for the Registration Act, have him be trained by Ms. Marvel or something would be cool.