Just because, here are the Hugo Award winners for Best Dramatic Presentation and Best Dramatic Presentation Long Form since 1968, so it at least gives some sort of idea of what the actual contenders were.
2003:
The Lord of the Rings: The Two Towers
2004:
The Lord of the Rings: The Return of the King
2005:
The Incredibles
2006:
Serenity
2007:
Pan's Labyrinth
2008:
Stardust
2009:
WALL-E
Obviously some television is mixed in there that confuses things, but from 2001 to 2009 there are 4 Best Picture nominees, including 1 winner, 2 winners of Best Animated Films, and 1 Best Foreign Language Film nominee and multiple winner of awards. Only Serenity and Stardust didn't garner any attention from the Academy.
Hardly perfect, but certainly suggestive that the stigma isn't as strong as it's been. Probably because Star Wars is over 30 years old now.
Year by Year:
1972 - A Clockwork Orange was nominated. Losing to The French Connection is nothing to be ashamed of.
1974 - Yeah, you can make a case for Sleeper. You can also make a case for Serpico, Last Tango in Paris, and Serpico of which none were nominated for Best Picture. Worth noting that genre picture The Exorcist was nominated.
1975- You can make a case for Young Frankenstein, although it did get a Screenplay nomination. Didn't help that Blazing Saddles was also a 1974 film. 3 of the BP nominees are classics in The Godfather Part II, Chinatown, and The Conversation, although Lenny and especially The Towering Inferno are not. Alice Doesn't Live Here Anymore and Day for Night were other notable films.
1976 - A Boy and His Dog isn't that good. Jaws was nominated for Best Picture.
1978 - Star Wars was nominated. Close Encounters was also something considered. Obviously one of the most famous horse races in Oscar history.
1979 - Superman could have been nominated. The fantasy Heaven Can Wait was up for a bunch of awards including Best Picture.
1980 - Alien could have been nominated, although the BP nominees of Kramer vs. Kramer, Breaking Away, Apocalypse Now!, All that Jazz, and Norma Rae certainly is pretty strong.
1981 - ESB certainly could have been nominated. Certainly it's a better movie than Tess. The other 4 nominees are pretty stout with Raging Bull, Ordinary People, Coal Miner's Daughter, and The Elephant Man rounding out the group.
1982 - Raiders of the Lost Ark was nominated. Probably should have won, although it took a long time for Spielberg to be accepted.
1983- E.T. was nominated instead of Blade Runner.
1984 - ROTJ probably didn't deserve a BP nomination.
1985 - 2010 didn't deserve a BP nomination.
1986 - BTTF certainly could have been nominated in a weak year. As could have Brazil and The Purple Rose of Cairo. And Kurosawa's Ran.
1987 - Sure Aliens could have been nominated. Probably wouldn't have beat Platoon or Hannah and Her Sisters, but certainly is a better movie than The Mission.
1988 - I'm fine with A Princess Bride not being a nominee.
1989 - Who Framed Roger Rabbit certainly is a notable omission. Big could also have contended.
1990 - Last Crusade or Batman certainly had cases, although I don't think either are top 5. Spike Lee's Do the Right Thing which wasn't nominated either and stands as a more glaring omission.
1991 - Edward Scissorhands has a case. The fantasy Ghost was nominated.
1992 - T2 could have been nominated, although it was competing with genre titles like Silence of the Lambs and Disney's Beauty and the Beast.
1994 - Jurassic Park certainly was notable, although obviously Schindler's List is the one that Spielberg campaigned behind.
1998 - Eh, Contact isn't a top 5 movie for me.
1999 - Yeah the Truman Show is kind of a surprising snub. It wouldn't have won, Saving Private Ryan and the Weinstein Shakespeare in Love campaign would have beaten it, but certainly it could have been nominated.
2000 - There were other notable movies besides Galaxy Quest, The Matrix for instance. Obviously The Matrix could have been nominated. And The Sixth Sense was nominated.
Obviously the Hugos aren't the whole story, but they tell us something about sci-fi / fantasy. From that list, I'd say that ESB, Aliens, BTTF, Who Framed Roger Rabbit, and The Truman Show are the ones with a real grievance. Obviously it's not complete, but those are the ones I'd start on first.