The make-at-home type: Mine is sort of like Wendy's chili, only more full of good things and better. But it's that style. I think my mother's was this way, which is why I gravitated toward it years ago, but I can also say with certainty that hers wouldn't have been very spicy or as full of interesting ingredients.
Chili for hot dogs and hamburgers: I grew to love the Tommy's and Carney's style of burger in L.A. The chili for things like that is not at all like what you'd eat in a bowl. Nathan's (of Coney Island) has a superb one. A Nathan's hot dog with chili and raw onions is bliss.
Cincinnati chili: A thing all its own, of course, and a life essential. I also used to get the chili and spaghetti at Bob's Big Boys in L.A., but I don't remember what theirs was really like. I'm sure it doesn't approach a Cincinnati. No sir. Cincinnati chili should also be a good one for the burgers and dogs, but I haven't yet tried that.
I used to get the "Chili Size" at Hamburger Hamlet, and I so wish I could bring back a solid memory of it.
If you go to a chili taste-off, the varieties are astounding. There are so many wonderful creations, it's hardly fair to even make a short list like this. I'd actually say most of them usually turn out to hold no interest for me, because I'm usually not into "chef-y" stuff, but I've had some beauties.