I quickly scrolled over this entire topic before, and from all glimpses I got I couldn't find a single mention of Analyze This (correct me if I'm wrong).

*Vito's shooting scene is reacted by Billy Crystal as the Don and Robert DeNiro as Fredo, as part of Crystal's dream
*after he tells DeNiro about this, Robert says: "I was Fredo? Don't think so"
*a meeting of all the NY families is hosted, when Billy Crystal acts as DeNiro's consiglieri, saying "baddabeep baddabap Betty Boop"

and there are some more small references to GF

on of the better references in You've got mail I think is when a musical piece just like the GF2 theme "A New Carpet" by Nino Rota is backing up a sequence of shots that suggests a quick time change, all of this after an entire dialogue about 'The Matresses'. The music there is very "Godfatherish" and it never occured to me before...