Poirot, by far, specifically as portrayed in the 1989 series, Agatha Christie's Poirot, which @Cy~ was gracious enough to introduce me to some time back. I've found the series an absolute joy to work my way through with her.
Beyond that, I would have to put Columbo in second place. I know he's not a classic detective in the same sense as Poirot or Holmes, but I find the way that he works to get under the skin of those that he's investigating to be downright beautiful.
Third place for me would go to Holmes, as portrayed in The Adventures of Sherlock Holmes, played by Jeremy Brett. The modern BBC series is okay, but it never did quite hit me in the same way as the older one, if I'm to be completely honest.