I needed the up-to-date list of iTunes categories (as of 2017) for a project but didn't find the list as a JSON anywhere. Here I'm sharing the latest categories list that I extracted from iTunes official page. I hope this helps someone.

itunes-category-list.json

{
    "1": {
        "name": "Arts",
        "sub": [
            "Design",
            "Fashion & Beauty",
            "Food",
            "Literature",
            "Performing Arts",
            "Visual Arts"
        ]
    },
    "2": {
        "name": "Business",
        "sub": [
            "Business News",
            "Careers",
            "Investing",
            "Management & Marketing",
            "Shopping"
        ]
    },
    "3": {
      "name": "Comedy",
      "sub": []
    },
    "4": {
        "name": "Education",
        "sub": [
            "Educational Technology",
            "Higher Education",
            "K-12",
            "Language Courses",
            "Training"
        ]
    },
    "5": {
        "name": "Games & Hobbies",
        "sub": [
            "Automotive",
            "Aviation",
            "Hobbies",
            "Other Games",
            "Video Games"
        ]
    },
    "6": {
        "name": "Government & Organizations",
        "sub": [
            "Local",
            "National",
            "Non-Profit",
            "Regional"
        ]
    },
    "7": {
        "name": "Health",
        "sub": [
            "Alternative Health",
            "Fitness & Nutrition",
            "Self-Help",
            "Sexuality"
        ]
    },
    "8": {
        "name": "Kids & Family",
        "sub": []
    },
    "9": {
        "name": "Music",
        "sub": []
    },
    "10": {
        "name": "News & Politics",
        "sub": []
    },
    "11": {
        "name": "Religion & Spirituality",
        "sub": [
            "Buddhism",
            "Christianity",
            "Hinduism",
            "Islam",
            "Judaism",
            "Other",
            "Spirituality"
        ]
    },
    "12": {
        "name": "Science & Medicine",
        "sub": [
            "Medicine",
            "Natural Sciences",
            "Social Sciences"
        ]
    },
    "13": {
        "name": "Society & Culture",
        "sub": [
            "History",
            "Personal Journals",
            "Philosophy",
            "Places & Travel"
        ]
    },
    "14": {
        "name": "Sports & Recreation",
        "sub": [
            "Amateur",
            "College & High School",
            "Outdoor",
            "Professional"
        ]
    },
    "15": {
        "name": "Technology",
        "sub": [
            "Gadgets",
            "Tech News",
            "Podcasting",
            "Software How-To"
        ]
    },
    "16": {
      "name": "TV & Film",
      "sub": []
    }
}

Very nice work! Though it seems like this list could be due for another revision, as the Podcasts Connect Help page currently lists 16 categories and this one lists 14. This list is missing Comedy as well as TV & Film.

@bertobox Thanks, I have updated the list.