2001, LOTR: FOTR should have won over A Beautiful Mind.
Of all the awards given out on the night, B. Picture is the only one that is not an artistic award and is not given to artists. It’s a business award that is given to producers for coordinating all the financial and artistic elements into a financially* and artistically successful film.
The realization of a story into cinema, coordinating all the artistic, financial, and production elements needed to make the film, is far greater for a film like LOTR than it is for ABM, especially given that ABM was, really, just another biopic while LOTR:FOTR was the creation of something new and unseen. Doing what has already been done before, regardless of how well it was done (ABM) is nowhere near the sort of achievement that was represented by LOTR:FOTR.
1998: Shakespeare In Love was a fine movie with great writing. On the other hand, no film nominated was as effective and as meaningful as Saving Private Ryan. Was SPR without flaws? No, but again, it’s the coordination of all production elements into an artistic and financial triumph that B. Picture represents, and none of the other films nominated came close to its level.
To comment on a couple of others…
1994: I think it’s a toss-up. The book Forrest Gump was a rather unlikeable story with an unlikeable character. The fact that the producers took that book and made one of the weirdest Hollywood films in history, and made it the biggest movie of the year, was just as amazing as Tarantino, Bender, etc taking their gangster tribute to French New Wave cinema and making more than $100m domestic.
Agree with 1996.
Though it hasn’t been mentioned yet, let me go ahead and defend 1997: Titanic should have (and did) win B. Picture. Again, the other films might have had elements that were “better” than Titanic, but, like I said, the coordination of all those elements in a production as vast as Titanic and making a very financially successful film out of it made it the slam-dunk obvious choice for B. Picture.
*No B. Picture winner has ever lost money. Only 1 B. Picture earned less than the average film released that year (2007’s The Hurt Locker.) From 1980-2007, over 80% of all B. Picture winners come from the top-two grossing films within the category (this changed when the # of nominees went to 10, btw).