Yes, when I first realized that being published in Japan by D3 Publisher was a common denominator between these weird and wonderful budget games that I found, I became very interested in them. My friends actually went to TGS one year and got everything they could from the D3 booth for me.

However, since I've moved to Japan, I've continued researching and collecting vintage games, and I've found that while the majority of Simple Series games were published by D3 Publisher, especially the PS2 games, there are also some titles that were officially published by other companies. I guess it all leads back to D3 somehow, though. Also, D3 Publisher was still independent in the years these games came out.

My favorites include (Almost all PS2):

• The Zombie vs Ambulance (aka Zombie Virus). Drive an ambulance around a zombie-infested city, rescuing survivors and upgrading your vehicle.
• The OneeChanbara series. Slay blood-gushing zombies as an inexplicably bikini-clad, cowboy-hat-wearing swordswoman with light adventure/Metroidvania elements. The earlier ones are better IMO; as time went on they focused more and more creepily on the sexy female characters which were initially mostly a gag, especially after the movie (Yes, a movie!) came out.
• RC de Go! (PS1) Race in a remote-control car league.
• The Sniper 2 (direct sequel to a PS1 game I own but haven't played). Play a sniper blackmailed into doing missions for a crime syndicate while you try to find a way out.
• The Ninkyo (aka Yakuza Fury). It's pretty fair to call this a very barebones Yakuza (Ryu ga Gotoku) knock-off, but it has its charms.
• The Nihon Tokushubutai (aka Special Forces). A strange hybrid of FPS and realtime strategy in which you control a SWAT team in various scenarios.
• The Helicopter (aka Radio Helicopter). Fly a radio helicopter around your neighborhood while completing arbitrary but fun challenges. There's another game that was marketed as "Radio Helicopter 2" in PAL territories, but it seems to be completely unrelated and not even a Simple Series game. I have it and didn't find it nearly as fun as the original.

There are more that look very interesting but I haven't played them yet, so I don't feel I can recommend them. And there are also some real dogs, naturally, although I should say that even the ones I've listed can be something of an acquired taste. The Earth Defence Force series started as Simple Series games too, although I haven't played any of them

While I was writing this I remembered a few more of my favorite budget games that weren't Simple Series games:

• Sanvein (aka Starfighter Sanvein) on PS1. I'm not normally one for overhead shooters but I was really taken with this one. There's an interesting light strategy element to it.
• TheDog Island on PS2 and Wii. Inspired by a line of stationery and decorative items, it's a collect-'em-up with light Metroidvania elements aimed at younger players, but quite fun and addictive.
• The Puppy/Kitty and the Magic Hat (aka Petz Dogz/Catz 2) on PS2 and Wii. A spiritual sequel to TheDog Island, they're actually two games which appear to be identical except that one is populated by dogs and the other by cats (I have the cat version).
• Choro-Q High Grade 2 (aka Road Trip Adventure). Choro-Q is a line of kids' toy cars that older Westerners may remember as Penny Racers. Naturally there is a whole slew of tie-in kids' games in Japan, from the Famicom onward, but for me this particular game is a standout. There's racing, sure, and it kind of sucks, yes, but the meat of the game is exploring a massive open world, solving mysteries, and figuring out how to get to various places and which special vehicle parts you'll need. It includes a "soccer" minigame which feels like a possible inspiration for Rocket League, but in a game that came out many years earlier.