Should they have won an Oscar?

When you're a so-called film fanatic (a rather self-proclaimed title, sadly), you can hardly avoid following the annual Oscar shows. Sometimes it's a bore and quite superficial, at other times it's surprising and deep. Apart from all the celebrity stunt stuff and expensive dresses and big names, the magic still lingers on (although, one wonder how long they can keep the magic going..). 

It's always a good way to get a rough picture of what's going on in the film industry of today. Of course, it's only the most prestigious award you can receive in this industry - not just for the American cinema but for all countries - and a lot of honour and money are being put into this award show. That shouldn't, however, overshadow the point of the show, which is, basically, to praise and honour the work of art and film making.

Yet, I haven't always agreed with the choice of winners/nominees of some categories (without sounding treacherous hopefully, I've always found the panel of judges rather suspicious whoever they might be). So it happens that I - in my mind, of course - pick my own nominees or winners (not that I claim to be particularly skillful as a judge in this matter), ones that - according to me - have been overlooked or overshadowed by others though time. I often look at the actors' acting in specific moments or at their overall performance during a movie. Are they thoroughly performances, how do they come across the screen and could anyone have done it better perhaps, etc.?

I have collected many favorite magical moments of brilliant acting (many of them are listed on my page "Actors/actresses at their best"). The question is always "WHY do you find him/her brilliant/interesting...?" and so on, but I feel I could write a book about that and it would take up a lot of space. So, I'm actually more interested in your opinions and have therefore listed a few examples below:

E.g.:
Should Tom Hanks have won (or at least been nominated for) an Oscar for his wonderfully hilarious performance in "A League of Their Own?

Should Natalie Wood have got one for her striking performance in "This Property is Condemned"?

Should Paul Newman also have had the chance to be nominated for his brilliant role in "The Sting"?

Could Yul Brynner have won an Oscar for his magnificent character in "The Journey" (1959) where he played opposite beautiful Deborah Kerr?

Or what about Audrey Hepburn for her captivating acting in "The Nun's Story" and/or "Robin and Marian"?

Perhaps you can come up with other examples?