John Hurt. I think he’s been nominated a few times in the past (nominated Best Actor for “The Elephant Man”), but no Oscar yet.
I have always felt, seriously, that Jeff Bridges is very underrated.
Edward Norton definitely deserves it the most though, IMHO.
I wouldn’t say he’s the best actor without an Oscar, but a guy who deserves some consideration is good ol’ Kevin Bacon, who’s never even been nominated. He’s turned in some brilliant dramatic work (Mystic River and Murder in the First) as well as some fine comedic performances (Tremors, e.g.). He should have at least received a nomination for Murder in the First, in my view, and I though his supporting performance in Mystic River was stronger and more subtle than the cartoonish turn by Tim Robbins (who actually won the Oscar).
Probably the best actor without an Oscar is Johnny Depp, closely followed by Gary Oldman and Edward Norton.
As for Actresses, I’d go with Laura Linney and Kate Winslett. Also, I think Madeline Stowe is a really fine actress who maybe didn’t get as many juicy parts as she should’ve over the years.
Oh yeah, and Mary McDonnell.
These are all excellent choices, but not really a “Morgan Freeman” in the bunch. No great actors PLUS very famous. Most of these are just excellent actors. So while there seem to be many great actors and actresses out there, the A-Listers who can actually act seem to be taken care of?
I agree with Gary Oldman mentioned above. I also think that Paul Bettany needs to get one for best supporting actor if nothing else. I mean come on - Dogville, Master and Commander, Beautiful Mind; lets face it the guy is in everything and he consistently does a great job.
I’d call Winslet, Depp, and McKellen “very famous.” (The same is true for several others in this thread, but those are the ones who immediately spring to mind as “A-listers.”)
Heh. I think we’re picking up on a Chris Rock distinction! 
Whoa re some other great actors that have never been nominated? I think Kurt Russell would qualify, even though he has done some clunkers, his work in Miracle this past year could have easily earned him a nod in my opinion.
49 posts and not one mentions Jon Heder
My first thought was Ian McKellan, but I see that others have beaten me to him. But how about Alan Rickman? I think it was a great tragedy that he wasn’t even nominated for Best Supporting in any of the Harry Potter movies. In fact, it doesn’t look like he’s been nominated for an Oscar at all (though he has a long enough list of other awards).
Was that for a screenplay? They hardly count anyway as they seem to give them away in breakfast cereal boxes… how else do you account for Damon & affleck having one? Or was it a technical award - the ones they hand out before the audience arrives…
mm
Good call on Bettany, although I have to admit I wouldn’t have remembered his name without you first posting it. He was fantastic in Master and Commander, and don’t forget about A Knight’s Tale 
Oh yes. I was wondering what she’d been up to lately. I adored her in Passion Fish and that Kevin Costner western.
Did Debra Winger ever win? She was one of the best things about 1980’s movies.
I would argue that Matt Damon earned his Oscar – Good Will Hunting was quite a good film, I think. I would also argue that Ben Affleck didn’t do much during that writing process except put his name on the cover and cash the paycheck.
Seconds to Chronos’ nomination (ha!) of Alan Rickman – if the Academy thinks Denzel Washington earned an Oscar for Training Day, then Rickman certainly should have won an Oscar for Die Hard. Seriously. That is one seriously awesome part, and extremely well-played!
Are you saying that for a reason other than “Ben Affleck is stupid?”
Oh come on. People are talking about Ian MacKellen and Kate Winslet and people with long, stellar resumes, and Jon Heder might be the best actor never to win an Oscar? He did one cult movie.
Pretty insulting to screenwriters. They give out two screenwriter awards each year, how is this like giving them out in ceral boxes?
Charlie Kaufman writing three of the most original movies in ages and winning one Oscar for it has to prove they give them out in cereal boxes. 
Actually, somewhere in between.
Despite getting 3 nominations for Picture, 4 for Director, and 5 for Screenplay, the only Oscar he won was for Visual Effects for 2001: A Space Odyssey, which is an artistic award, but in a technical field.
Now obviously, 2001 deserved this Oscar (amazingly, the only one it won), but the problem is that Kubrick didn’t do more than design, or conceptualize, the effects. He didn’t actually execute them, beyond his capacity as director and de facto supervisor of the production.
This would be similar to giving George Lucas the Visual Effects Oscar for Star Wars or Spielberg the V.E. Oscar for E.T.. What’s even worse is that, by having Kubrick assume credit for the work of the actual V.E. supervisors, it prevented some deserving people (especially Douglas Trumbull, who’d go on to do Close Encounters’s effects) from ever winning.
Better than 0-for-3. I wouldn’t given him the Oscar for the other two anyway, but he was certainly richly deserving of this one (his best, too) and the Academy suitably delivered. A little justice does squeak through on occasion.