A supporting cast (Like Betty, Ned, Liz, Flash, Harry, Robbie, Glory, Pete's neighbors and landlords, Mary Jane's friends, Felicia, etc) and all the drama with their lives. Yea, the soap opera stuff neatly woven around the action. I love it.
Peter progressing through life stages and lessons... you know, like most of us do. (A caveat would be: Don't kill Aunt May) He would naturally stay married to MJ (he IS after all a responsible, decent guy, who was marriage-minded early on) but someday let them have kids.
A strong, smart Peter, whose Spider-sense actually works, unless there is a reason given... you know, like his has the flu, etc.
A Peter who wholeheartedly loves his wife, sans mental obsession with a long dead girlfriend. Peter went through the stages of grief. Even though Gwen will always be special to him, he really moved on. He's completely into MJ.
Art on the realistic side, as opposed to the cartoony... I hate the freaky, buggy, scrawny Spidey. (JR Sr. was closer to a Deodato in realism than to Jrs. And has anyone else thought that JR Sr.'s Peter had a sight resemblance to Elvis?)
A more secret secret-identity. Finding out who he is should be a bigger deal.
Webbing that doesn't break. It used to be such tough stuff... now everyone and their dog seems to be able to snap it.
Continuity. Even references to past issues, so we know they are paying attention.
Shorter stories, at least now and then. I don't mind the 6-parters, but how about a stand alone now and then, or a TPB with two 3-part stories? Of course, there should always be the relationship threads that are on-going.
The Letter's page. I love reading these in the old issues.