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Rory- ISFJ or INFJ. She's mostly even tempered but still a bit sensitive. Rule follower, though not religiously like Paris. And she's like a very nice, very quiet, goody-two shoes type. She's always worried about people being nice and considerate to one another, which seems deliberately Fe.
Lorelai- ENFP or ENFJ. Ive also heard it suggested that she might be ESFP. Personally I'm leaning ENFP just because being scatterbrained + very mañana + verbally quick + really sensitive seems more like ENFP than ENFJ. Plus she can get all weird towards the objects of her affection, which seems very Fi. And, finally, she does that NFP thing where she keeps her feelings to herself (though badly) and then explodes later. Oh and she's not really too worried about offending others if her feelings come first.
Luke- ISTP or INTJ. I am iffy on the N because he's so handy-man trade-school-ish.
Emily- ESFJ. She barely ever gets her daughter's jokes or humor.
Richard- ISTJ. Quiet rule-follower that likes his quiet time.
Dean- ISTP. He builds cars and has no ambitions. And he's got some anger control issues.
Jess- INFP. Annoying, though. Whiny.
Sookie- ESFJ. For sure.
Taylor- ESFJ. Gone wrong.