A chili dog is a hotdog with something resembling chili on it, and it can be a wonderful thing if it's done right. Much depends on the quality of the "chili"; to my mind, the chili is more important than the dog itself. Of course, it may just be that the quality of the "chili" tends to vary more than that of the dog. It's only for the sake of convenience that I use the term "chili" to refer to this substance; I apologize to those who know better.
The chili dogs I'd recommend most heartily are those sold by the Nathan's chain and those sold by the 7-11 convenience store chain. They're both delicious, though Nathan's has a slight edge due to a closer resemblance to actual food. The difference between the two lies in the "chili".
Nathan's "chili" is a relatively thin sauce with beans and soft pieces of something that signifies "meat". The flavor is pleasing, somewhat sweet, and mildly spicy. The "bean" signifiers appear to be actual beans.
7-11 stores offer a more fine-grained "chili", something like a large-grained paste. My belief is that the granular material is mostly derived from soy beans, with a leavening of "meat by-products" to add character. The flavor is spicier than the Nathan's product. If you've had Hormel "chili", it's very similar. 7-11 stores are far more common than Nathan's, so this may be your only realistic option.
Chili dogs go well with an authoritative ale, like Ipswich Ale, Otter Creek Copper Ale, or Magic Hat Blind Faith. Any decent India pale ale (IPA) should be adequate in time of need. If you choose the 7-11 product, try to get something hoppier than those: Due to the greasiness of the food product, you'll want a well-hopped beer. I had some Anchor Liberty Ale recently which would have been just about ideal for the purpose.
sockpuppet suggests Harpoon IPA, and I agree: It's fashionable around Boston to sneer at Harpoon because they've got this ubiquity thing happening, but they deserve more respect than that.
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