In what industry? I’ve done many hundreds of interviews (software engineers and related roles) and received maybe five thank you emails. It never consciously factors into my decision, but it does make me feel slightly worse about the candidate in a that’s-kind-of-pathetic sort of way. I like to think I still make an objective decision, but who really knows…
A brief e-mail is appropriate. Use it as an opportunity to succinctly reinforce your interest and most outstanding qualifications.
Something along the lines of, “Dear X, Thank you for meeting with me yesterday. I enjoyed the opportunity to learn more about Acme’s work, especially since it dovetails so nicely with my widget-building experience in Pago-Pago. I hope I will have the opportunity to contribute to Acme’s design of widget 2.0. Sincerely, XX.”
I agree with dalej42 and Voyager that a handwritten note is not a good idea in this day and age. It also reeks of desperation - there’s making an effort with respect to things that matter, and then there is trying too hard to stand out with respect to a relatively trivial detail.