Martin Scorsese:
Be sure to check out Alice Doesn't Live Here Anymore too.
Ingmar Bergman
Haven't seen much of his myself, but add Persona to the list. I'd start off with Wild Strawberries or The Seventh Seal before that though.
Animation
Studio Ghibli is your friend. After those you mentioned My Neighbour Totoro is a must-see (and my personal favourite). For more anime also check out Millenium Actress.
There's also Belleville Rendez Vous / The Triplets of Belleville - bizarre and mostly silent French comedy from a few years back about the Tour de France, the Mafia and an overweight dog. Hilarious!
Screwball Comedies
Some crackers there already but don't forget His Girl Friday, Arsenic and Old Lace and Monkey Business (all starring Cary Grant). The Whole Town's Talking with Edward G Robsinson and Jean Arthur is pretty funny. Also see some Billy Wilder: Ninotchka (he scripted it), Some Like It Hot, The Fortune Cookie and A Foreign Affair. Hell, watch as many Wilder films as you can period. OH and don't you dare forget It Happened One Night (Capra / Gable treat winning the big 5 Oscars).
Film Noir
Saving the best for last here. After those you listed (which are all ace) there's also:
M (Fritz Lang and Peter Lorre in one of the very first, excellent)
The Maltese Falcon (regarded as the first American noir, Bogart's big break and John Huston's debut. START WITH THIS)
The Big Sleep (Bogie and Bacall in their best pairing but a bloody confusing plot)
The Postman Always Rings Twice (good companion piece to Double Indemnity, which is my fav btw)
Laura
Where the Sidewalk Ends (a pair of Otto Preminger, Dana Andrews and Gene Tierney teamings - I love Gene Tierney, check out more of her's like Whirlpool and The Ghost and Mrs Muir afterwards)
Scarlett Street (Lang again with Edward G, brilliant and devasting)
The Big Heat (more Lang, pretty hardcore for the time)
The Night of the Hunter (Charles Laughton's only film as director, black as Hell and VERY iconic)
Suspicion
Notorious (pair of Hitchcock's both with Cary Grant, Notorious in particular being absolutely gripping)
The Killing (an early Kubrick)
Touch of Evil (regarded as the last true noir of the period - 40s to 50s - and directed by Mr Welles himself)
I'm biased towards the screwballs and film noir because I adore Golden Age Hollywood (30s through 50s anyway) and there are so many gems waiting to be discovered there. Best thing to do if you're keen on starting afterwards is picking a few actors and directors and working through them (Cary Grant, Jimmy Stewart, Bogie, both Hepburns, Hitch, Huston, Howards Hawks and Wilder for example) and going on from there. I could probably list about 50 must sees from that lot off the top of my head. The 50s are really interesting because you have all these old school talents mingling with the new generation of Marlon Brando, Paul Newman, Jack Lemmon, Marilyn Monroe, Grace Kelly, Sidney Lumet, Kubrick and Eli Kazan. It was such a ripe period for talent and many landmark films came out.
EDIT
LOL didn't mean to write that much. There's a fair few of yours I haven't seen but can't join in with you as I'm between (free) rental accounts right now. Overall you've got a very good selection for each genre / director, it's just there's always so much more to each genre and not enough space to write it all.
And also, Westerns are well worth a look if you get time. Classics such as Rio Bravo, The Searchers, Red River, Fort Apache, My Darling Clementine, Destry Rides Again and Winchester '73 are just some of those that came out before Sergio Leone came along and changed them forever. They range from fun in the 30s, epic in the 40s to pyschological in the 50s. Watch some of the Jimmy Stewart / Anthony Mann westerns and you'll see where Jimmy's nice guy persona was first warped before Hitch took it further.