There are a ton of short story collections, does anyone know if there are repeat stories in them? I know there’s Bradbury Stories, The Illustrated Man, The Toynbee Convector collection, and a ton more. Does anybody know one way or the other?

Not only are there at least some repeats in collections, but related stories were expanded into novels so you will come across the same stories not only more than once but sometimes in altered form. The novels also contain original passages.

Here is a complete list of stories, including collections in which they appear and title changes.

http://www.bradburymedia.co.uk/storiesDB.htm

dandelion has linked a good list by dr Phil Nichols, and I have also made exhaustive lists of Ray Bradbury's stories, if you need to know more.

However, you can capture 200 of Ray's best stories by buying just two books:

The Stories of Ray Bradbury (Knopf, 1980), and

Bradbury Stories: 100 of His Most Celebrated Tales (William Morrow, 2003).

Between those two, there is no duplication whatsoever, and as I say, there are 100 stories in each. They are both retrospectives that duplicate stories in Ray's original story collections, but each contains a few stories that were not in the original collections.

If you'd like to read Ray's original story collections, there were fifteen major collections (which I define as collections consisting entirely or mostly of previously uncollected stories):

1. Dark Carnival (Arkham House, 1947)
2. The Martian Chronicles (Doubleday, 1950)
3. The Illustrated Man (Doubleday, 1951)
4. The Golden Apples of the Sun (Doubleday, 1953)
5. The October Country (Ballantine, 1955)
6. A Medicine for Melancholy (Doubleday, 1959)
7. The Machineries of Joy (Simon & Schuster, 1964)
8. I Sing the Body Electric! (Alfred A. Knopf, 1969)
9. Long After Midnight (Alfred A. Knopf, 1976)
10. The Toynbee Convector (Alfred A. Knopf, 1988)
11. Quicker Than the Eye (Avon, 1996)
12. Driving Blind (Avon, 1997)
13. One More for the Road (William Morrow, 2002)
14. The Cat’s Pajamas (William Morrow, 2004)
15. We’ll Always Have Paris (William Morrow, 2009)

Bradbury' bibliography is very complicated! Even if you read all the books listed here, you still won't have read all his stories! Note also that The October Country consists mostly of revised versions of stories in Dark Carnival. Other than that, the "major" fifteen story collections contain so little duplication that it isn't even worth mentioning.

Both dandelion and douglasSP have provided excellent information. I thought I would add one more source containing very good bibliographic information about Ray's work, including both original and later publication sources and dates. It is the Internet Speculative Fiction Data Base (ISFDB). Here is a link to that site's summary bibliography for Ray Bradbury:

http://www.isfdb.org/cgi-bin/ea.cgi?194+None