In addition to Cordoza’s interesting examples, here are some analytical questions about 'racism in fiction'. These are not about content but about form.

Are racist notions in the story opinions attributed to certain characters?
Are they expressed in dialogue? Do they show up in thoughts?
If so, which characters hold the racist notions? Are there characters who disagree?
Does the plot ‘show’ that a racist stereotype is ‘true’?

Here’s a text sample in different forms. Yahoos are humans; Houyhnhnms are horses. For Houyhnhnms, Yahoos and Europeans, just insert any ‘superior’ and ‘inferior’ groups you wish!

(1) Yahoo as I am, it is well known through all Houyhnhnmland, that, by the instructions and example of my illustrious master, I was able in the compass of two years (although I confess with the utmost difficulty) to remove that infernal habit of lying, shuffling, deceiving, and equivocating, so deeply rooted in the very souls of all my species; especially the Europeans.
Original quote from Jonathan Swift: Gulliver’s Travels.
Narration in first person; the ‘inferior’ speaks about himself; subject and object are identical.

(2) The master horse addressed the audience.
‘Yahoo as he is, by the instructions and example of me, his master, he has been able in the compass of two years (although with the utmost difficulty) to remove that infernal habit of lying, shuffling, deceiving, and equivocating, so deeply rooted in the very souls of all his species; especially the Europeans.’
Dialogue; the ‘superior’ speaks about the ‘inferior’.

(3) Yahoo as he was, by the instructions and example of his illustrious master, he was able in the compass of two years (although with the utmost difficulty) to remove that infernal habit of lying, shuffling, deceiving, and equivocating, so deeply rooted in the very souls of all his species; especially the Europeans.
Narration in third person. The notions are presented as facts.

(4) ‘It wasn’t me! I didn’t do it!’ he protested, hoping that they would put the blame on some other worthless Yahoo.
It was another contemptible display of that infernal habit of lying, shuffling, deceiving, and equivocating, so deeply rooted in the very souls of all his species; especially the Europeans.
The plot confirms the stereotype. The narration generalises it.

(1) and (2) present subjective opinions, (1) a case of slave mentality, (2) a master talking about his pet.
(3) and (4) present the notions as ‘true’. (4) is by far the strongest example because it not merely says so, it shows.

There's a difference whether a story contains characters who have racist opinions, or whether characters act according to racist stereotypes and thus ‘confirm’ them. (Now if you are looking for further interesting times, insert ‘sexist’ instead of ‘racist’ in this sentence and apply it to a selection of stories.) This does not actually solve the ‘racism in fiction’ question, it just differentiates it somewhat.

Like Mobius and redEva, personally I would be happy to see more interracial stories that are simply interracial. Without the bigotry and without the racism. It appears, however, that racist stereotypes for some writers and readers work as a fetish of its own?