Have you used deities from real-world pantheons, from D&D fictional pantheons, or your own custom deities?
In terms of religion, I early on adopted a feel from Robert Howard or Fritz Leiber of a world with many many deities, and the feel of Greek myth where heroes regularly interact with deities. I came up with this notion that there were 1000 gods - a number so large I'd never run out of room for creativity. Occasionally when I was very young I would borrow a real world deity or one from Greyhawk, but I usually just invented them on the spot when I needed a new evil cult (and kept poor notes). However, gradually certain invented deities became reoccurring - Lado the Builder, Aravar the Traveller, Usurl God of Death, Sormkortek God of Rats, and so forth.
If you have used real-world deities or pantheons in your D&D campaigns, which ones?
I honestly can't recall, but in an organized fashion, then no. Some names may have slipped in during my games before 8th grade or so when I started to formalize my homebrew, but I can't recall which. I'm real world religious and I know wrestled with this question back as early as 6th grade as what was the most appropriate way to approach religion in the game. I decided it was by far the safest to make sure everything was obviously unreal and invented, and at some level unserious. Importing my own religious beliefs in the game would be blasphemous. And while I really didn't think I would be offending gods I didn't believe existed, I knew people who were pious Hindus and of other faiths, and I didn't want to offend them. So I extended to them the same courtesy that I wanted myself. As a highly polytheistic setting, there are elements of the style and presentation of the religion that I borrow from real world polytheism, particularly Greek and Hindu, but I try to never go as far as do even a pastiche of a real world religion.
Do you stick to one source per fantasy world (e.g. Greek deities only or FR deities), or do you mix deities from different sources (including possibly your custom)
I mix. The latest iteration includes a large number of my homebrew deities, a few Greyhawk deities (goblin, elven, and dwarf deities), and a few deities from Green Ronin's 'The Book of the Righteous'.
Do you allocate separate pantheons in your fantasy world, depending for instance on location or race (e.g. a Northern and a Southern pantheon, Dwarves worship the Norse pantheon, Elves have elven deities...)?
There are so many gods no one region or city worships them all, but usually each city selects 6-12 as official patrons that they in turn patronize. Most nations in turn also have a national patron deity. But which gods a region or city worships and which they consider alien isn't really divided along ethnic or regional lines, but simply one what is important to that regions history and most of all economy. Mining towns the world over are going to worship one or more chthonic deities, and probably one or more gods of metalworking. Farming towns are going to worship gods of sun, agriculture, and water. Mercantile towns worship gods of trade, industry, and travel. Cities and regions have a particular character, so one might worship a chaotic god of earth, and another a lawful god of earth. One might worship a good god of death, and another an evil one. One might worship the god of cunning and deceit, and another a good of justice and fairness. And it's a sort of hodge podge that is dynamic and always changing. The chaotic evil god of storms is always working to supplant the chaotic good god of water in the favor of the people, and so forth.
I do largely divide the pantheons on the basis of race, but even that isn't perfectly clear cut because the different racial pantheons are intermarried and/or interbred, so that one deity might count as being in two pantheons or a town might worship a consort of a deity that is normally considered to belong to a different racial group. Also in areas with a racial minority, a deities cult might end up crossing racial lines. The gods themselves largely act as if they were all of the same race with separate families. The dynamics are somewhere between a dystopian portrayal of the suburbs and Game of Thrones.
Have you used non-deities-based religions in your fantasy world?
No. I want a distinctly ancient feel to the world, like something that reflects in a way bronze age culture. Modern and post-modern conceptions of religion I don't feel have a place in what I'm going for.