According to Granny Smith's tale in Family Appreciation Day, his grandfather, "Stinkin' Rich', was one of the first ponies to buy Granny Smith's zap apple jam, and started a business by reselling it. In the same episode, it was told that this had helped contribute to the foundation of Ponyville.
In the same episode, Filthy Rich appears at Sweet Apple Acres to politely confirm he will receive the first one hundred jars of zap apple jam from Granny Smith, "as usual". As they walk off-screen, Granny asks him how his father is doing. He is later seen giving a presentation about "Rich's Barnyard Bargains" to Apple Bloom's class that bores most of the class to sleep except for Twist and Diamond Tiara. He is again seen at the end of the episode sternly pushing a reluctant Diamond Tiara to Sweet Apple Acres to help other fillies sing to the water in the watering cans, part of Granny Smith's special process of making zap apple jam. Despite being a rich business pony and his daughter's mean spirit, Filthy is amicable to Apple Bloom, Granny Smith and everypony else.
When Granny Smith calls him by his first name, he explains that he prefers "Rich". Cheerilee initially calls him "Mr. Filthy"; after he looks chidingly at her she immediately corrects herself, and he regains his usual easy going and calm appearance.
In Pinkie Pride, Diamond Tiara refers to him in the song Pinkie the Party Planner.
Filthy Rich appears in Testing Testing 1, 2, 3 as Rainbow Dash depressingly flies over him as he buys a whole crate of apples from Big McIntosh.
Filthy Rich appears in Inspiration Manifestation next to his daughter Diamond Tiara at the fair.
In comic, Filthy Rich is mentioned, and a "Future Site of a new Barnyard Bargains" billboard featuring a waving image of him appears.
On page 13 of comic, Summer van der Hoof says that Filthy Rich "was seen eating a creme de menthe sundae!"
My Little Pony mobile game description
The father of Diamond Tiara, Filthy Rich is a wealthy businesspony whose family contributed to the foundation of Ponyville.
Enterplay's Trading Card description
Filthy Rich is just about the best salespony in Ponyville! He's the owner of Rich's Barnyard Bargains, not only an excellent store to buy somepony a gift, but also the first place to go to purchase some of the Apple Family's world famous Zap Apple Jam. Raising a pony as "spirited" as his filly Diamond Tiara is a lot of work, but luckily this pony is rich with wealth and patience. Just remember not to call call him Filthy; he prefers Rich!
"...And that's how Rich's Barnyard Bargains became the cornerstone of retail in Ponyville!" -Filthy Rich
His card is the #25 of Series 2, and groups him with Stinkin' Rich and Diamond Tiara.
The Elements of Harmony guidebook
FILTHY RICH and his wealthy family date back to the very founding of Ponyville. His daughter is Diamond Tiara.