One that comes to mind is Paper Moon, the funeral isn’t exactly the first scene, but close enough.
The Big Chill? I remember it started with what turned out to be Kevin Costner’s character’s corpse being dressed for a funeral.
Chariots of Fire (1981) begins and ends at the funeral of Harold Abrahams (I’d say that the film properly ends as Lindsay and Montague leave the church, even though a reprise of the flashback “running on the beach” scene is used for the end credits).
I think that Harold and Maude (1971) probably starts at a funeral, but I can’t remember it clearly enough.
Great thread subject, ccwaterback! There are sure to be some good movies that show up here…
Evita begins (more or less) with Evita’s funeral.
Unforgiven - I believe the first scene in the movie is of the tree on the hill that overlooks his wife’s grave. Not exactly a funeral, but it’s the best I can do at this hour.
Thanks Antonius Block. I just happened to be gawking at the boob tube last night when a movie was just starting. The very first scene was a funeral gathering around a burial plot. I think there’s a lot of movies that start out with funeral scenes, we will see. 
Sleepless in Seattle - begins with the funeral of Tom Hanks’ wife.
Terms of Endearment almost has a funeral as the first scene, but not quite. There’s a very short scene first of Aurora with the baby before it cuts to the aftermath of her husband’s funeral.
Support Your Local Sheriff begins with a funeral, and when the mourners notice glitters of gold in the gravesite, fights break out and a goldrush in the small town ensues.
To Die For, directed by Gus Van Sant.
A couple of James Bond movies did – Thunderball starts at the funeral of someone with the intials “JB”, and you’re meant to think it was James Bond, only it’s really Jacques Bouvoir, and he’s not treally dead, either.
For Your Eyes Only also starts out with the funeral of JB, but this time it really is James Bond. Only he’s not really dead, it’s just a ploy to get his enemies off his track. This idea was copied from Ian Fleming’s book (the obit in the book provided JB fanboys with a lot of biographical info), one of the few points of resemblance between the book and the film in this case.
For some perverse reason, the early Bond films liked to start with the notion that Bond was killed in the teaser. In From Russia With Love we apparently see Bond getting snuffed by assassion Red Grant – only it;s mot really Bond, but a guy wearing a mask in a practice session for Grant.
Why did they do this? It’s a James Bond film, fer cryin’ out loud! We know they can’t kill him off in the first 5 minutes. They’got 90-120 minutes to fill!
Charade.
Mistake there – I meant You Only Live Twice, not For Your Eyes Only
The Village.
It’s been a long time since I saw it, but Hitchcock’s “Family Affair” maybe?
The Comic starts with the funeral of the Dick Van Dyck character.
I seem to recall Let’s Not Talk About All These Women started with a funeral, but it’s been over 30 years, so I’m not entirely sure. It is a fascinating film: a pure slapstick comedy directed by Ingmar Bergman.
Do you mean “Family Plot?” If so, that doesn’t start with a funeral, but with the a jewell theft.
No, Harold and Maude doesn’t begin with a funeral, it begins
With Harold’s first “suicide” by hanging.
Pretty memorable, IMO.
Witness
Immortal Beloved, the film about Ludwig van Beethoven begins with his funeral.
I wonder if Lawrence of Arabia counts — it opens with Lawrence’s ill-fated motorcycle ride, and then the memorial service at the cathedral.
**Lawrence of Arabia ** opens with Larry getting killed on his motorcycle, but quickly shifts to the mourners leaving his memorial services.